Evaluating an exponential function The function gives the value of a home in dollars in the year 1980 + t. What was the value of the home in 1988? Round your answer to the nearest whole dollar amount and give

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  1. college calc

    Give a formula for the function illustrated using a vertical shift of an exponential function. The two points marked on the graph are A=(−1,17) and B=(1,2). The red horizontal line is given by y=1, and is a horizontal asymptote of the function. What is

  2. Exponential Growth and Decay

    Can somebody please check my answers? 1. Identify the initial amount a and the growth factor b in the exponential function. g(x)=14*2^x a)a=14, b=x b)a=14, b=2

  3. calculus

    Suppose that the sales at Borders bookstores went from 68 million dollars in 1990 to 427 million dollars in 1995 . Find an exponential function to model the sales (in millions of dollars) as a function of years,t, since 1990.

  4. calculus

    Give a possible formula for the illustrated function using a vertical shift of an exponential function. The two points marked on the graph are A=(−172) and B=(10). The red horizontal line is given by y=−3, and is a horizontal asymptote of the function

  5. math

    Give a formula for the exponential function . The two points marked on the graph are A=(−1−43) and B=(12). The red horizontal line is given by y=5, and is a horizontal asymptote of the function.

  6. math

    Plz Help 1. what is the end behavior of the exponetial function f(x)=3/2*(4/5)^x? 2. use a graph to determine if the exponential function g(x)=-6*5^x is positive or negative and increasing or decreasing

  7. Calculus

    In order to express the function y=12^19x+7 as a composition of two functions the outer of which is an exponential function,we would let u be equal to the inner function, u=19x+7, and then write y as a function of u, as follows: y= ??? . (b) In order to

  8. Math help and check

    Which kind of function best models the set of data points (–1, 22), (0, 6), (1, –10), (2, –26), and (3, –42)? linear **** quadratic exponential none of the above 2. Which kind of function best models the set of data points (–3, 18), (–2, 6),

  9. Algebra

    Can someone help. Is the function below exponential? 𝑚(𝑡)=(2⋅5𝑡)3 If so, write the function in the form 𝑚(𝑡)=𝑎𝑏𝑡 and enter the values you find for 𝑎 and 𝑏 in the indicated blanks below.If the function is not exponential,

  10. calculus please help asap

    true or false questions: a)The derivatives of the reciprocal trigonometric functions can be found using the chain rule and their related base functions. b) A sinusoidal function can be differentiated only if the independent variable is measured in radians.

  11. Algebra

    Myra uses an inverse variation function to model the data for the ordered pairs below. (2, 30), (3, 20), (4, 15), (5, 12), (6, 10) Which statement best explains whether an inverse variation function is the best model for the data? An inverse function is

  12. Calculus

    A company decides to begin making and selling computers. The price function is given as follows: p=−70x+4000, where x is the number of computers that can be sold at a price of p dollars per unit. Additionally, the financial department has determined that

  13. Math

    Is the function below exponential? G(t)=(5⋅t)^2 If so, write the function in the form G(t)=ab^t and enter the values you find for a and b in the indicated blanks below. If the function is not exponential, enter NONE in both blanks below. a= b=

  14. algerbra

    Belinda wants to invest $1000. The table below shows the value of her investment under two different options for two different years: Number of years 1 2 3 Option 1 (amount in dollars) 1300 1600 1900 Option 2 (amount in dollars) 1120 1254.40 1404.93 Part

  15. Algebra

    Which of the following statements is the best description of exponential decay? A. Exponential behavior occurs when a function increases at a rate of increasing value. B. Exponential behavior occurs when a function increases at a rate of decreasing value.

  16. Math

    An exponential function with a base of 3 has been vertically stretched by a factor of 1.5 and reflected in the y-axis. Its asymptote is the line y=2. Its y-intercept is (0,3.5). Write an equation of the function and state its domain and range.

  17. calculus

    The function y=f(x) graphed above is assumed to be a vertical shift of an exponential function. The two points marked on the graph are A= (-1,-31) and B= (1,-1) . The red horizontal line is given by y= 1, and is a horizontal asymptote of the function. Give

  18. Algebra

    John is thinking about buying a house for $179,000. The table below shows the projected value of two different houses for three years. Number of years 1 2 3 House 1 (value in dollars) 186,160 193,606.40 201,350.66 House 2 (value in dollars) 190,000 201,000

  19. Algebra

    Describe how an exponential function changes as the base increases. What is an "exponential function" and how would I find the answer? Thank you! :-)

  20. Algebra

    Two different businesses model their profits over 15 years, where x is the year, f(x) is the profits of a garden shop, and g(x) is the profits of a construction materials business. Use the data to determine which function is exponential, and use the table

  21. algebra

    Given the exponential function A(x) = P(1 + r)x, what value for r will make the function a decay function?

  22. math

    3. Write the exponential growth function to model the following situation: A population of 422, 000 increases by 12% each year. 4. At t = 0 there are 50 grams of a radioactive isotope. The isotope has a half-life of 16 minutes. Use the exponential decay

  23. math

    (a) In order to express the function y = 1010 x + 4, as a composition of two functions the outer of which is an exponential function, we would let u be equal to the inner function, u = , and then write y as a function of u, as follows: y = . (b) In order

  24. mathematics

    The exponential decay graph shows the expected depreciation for a new boat, selling for $3500, over 10 years. A coordinate graph is shown. The horizontal axis extends from 0 to 12 years. The vertical axis extends from 0 to 9500 with an axis label of

  25. Math

    a) In order to express the function y = 1311 x − 4, as a composition of two functions the outer of which is an exponential function, we would let u be equal to the inner function, u = , and then write y as a function of u, as follows: y = . (b) In order

  26. math

    The value of Sara's new car decreases at a rate of 8% each year. 1.Write an exponential function to model the decrease in the car's value each month. 2.Write an exponential function to model the decrease in the car's value each week. 3.Write an exponential

  27. Its just math bro

    Joe bought an apple tree that was 48 inches in height. He noticed that this tree grew approximately 4 inches in height each year. Which statement best describes the function that could be used to model the height of the apple tree, h(t), as a function of

  28. Math

    x 3 6 9 15 21 f(x) 7.79 9.426 11.405 16.699 24.448 If the function is linear or exponential, write a formula for it below. If the function is neither, enter NONE.

  29. Math Functions

    Write two equations to represent the same exponential function with a y-intercept of 5 and an asymptote at y=3 . Investigate whether other exponential functions have the same properties. Use the transformations to explain your observations.

  30. Algebra

    Two different businesses model their profits over 15 years, where x is the year, f(x) is the profits of a garden shop, and g(x) is the profits of a construction materials business. Use the data to determine which function is exponential, and use the table

  31. Algebra 1

    Which of the following statements is true about the function y = 5⋅x4 ? It is an even function It is an odd function It is an exponential function It is an inverse function

  32. Math

    Is the function below exponential? q(r)=−8/3^r If so, write the function in the form q(r)=ab^r and enter the values you find for a and b in the indicated blanks below. If the function is not exponential, enter NONE in both blanks below. a=-8 b=??

  33. horizontal asymptote

    Find the horizontal asymptotes of the function's graph y = 200 / (1+10e^(0.5x)) If you let x --> minus infinty the exponential tends to zero and the function approaches 200. If x --> infinity then the exponential becomes infinite and therefore the limit is

  34. Math

    Redo problem 13 from section 1.8 of your textbook (page 62), but use the functions in the questions below rather than the functions in your textbook: (a) In order to express the function y = 1311 x − 4, as a composition of two functions the outer of

  35. mathematics

    3. A vacation home in Orlando, Florida, rents for $105 per day. The function f(x) = 105x gives the cost of renting the home for x days. What is the domain of this function?

  36. pre calc

    The Identity Function The Squaring Function The Cubing Function The Reciprocal Function The Square Root Function The Exponential Functional Lo The Natural Logarithum Function The Sine Function The Cosine Function The Absolute Value Function The Greatest

  37. Calculus

    The Picture It frame company determines that the cost function for its new make-at-Home picture frame is: C(x)= 60x + 72,000, where x is the number of frames produced and C(x) is the cost in dollars. The revenue function for the same freame is:

  38. Algebra-Mathmate or Reiny or Dr. Bob, please check

    I have two short questions which I think I know the answer-could you please check? If I write log(b)x - 2log(b)y as a single logarithm it would be log(b) x/y^2, correct? If not please help and Is the function f(x) = 1/x a exponential function -I think it

  39. Pre - CALCULUS

    For the data set shown by the table, a. Create a scatter plot for the data. (You do not need to submit the scatter plot) b. Use the scatter plot to determine whether an exponential function or a logarithmic function is the best choice for modeling the

  40. calculus

    Constant annual percentage growth The function gives the value of a home in dollars in the year 2000 + t. Find the constant annual percentage change in the value of the home. Give appropriate units with your answer. Again, I'm not sure what function is

  41. Math

    Which combination could create the function f(x)= x√x? adding a rational function and a linear function adding a linear function and a logarithmic function multiplying a linear function and a square-root function dividing an exponential function and a

  42. Calculus HELP ASAP

    Listed below are four types of functions. Which does not possess a derivative of the same type? a) exponential function b) logarithmic function c) sinusoidal function d) linear function e) NO RESPONSE

  43. Algebra

    Which are the correct answers? In a certain candy factory, the amount of candy bars produced annually is double the amount from the year before. This relationship can be described by: Select one: a. a linear function b. an exponential function Question 5

  44. math

    is y=2^x^2 considered a double exponential function or not? I believe it is but am not sure since the exponent is x and that is squared. I think to qualify as exponential function wouldn't the x need to be a number and not x?

  45. Algebra

    Explain how you would determine whether the graph of y = x^4 represents an exponential function. What is an exponential function? Thank you! :-)

  46. Math

    If Joe wanted to create a function that modeled an exponential function with base of 8 and what exponents were needed to reach specific values, how would he set up his function? f(x) = x^8 f(x) = log8 x f(x) = logx 8 f(x) = 8^x

  47. Math

    I don't even know where to begin on this problem... The function f(x) is an unshifted exponential function which goes through the oints (2,5) (3,4). a)What is the equation for f(x)? b)write f(10) and f(100). If it's an exponential function then we know

  48. Math

    So I figured out how to do the first 6, how do I do the remaining? 7. Evaluate the function below over the domain {-1, 0, 1, 2}. As the values of the domain increase, do the values of the function increase or decrease? y = (3/4)ˣ 8. Suppose an investment

  49. calculus

    I am confused on how to write this function as an exponential function having a base 10: P(t)= 50e^(0.5t). The answer in my textbook is: P(t) =50(10)^(t/4.6)

  50. Algebra

    x | y /////////// x | y 0 | -3 ////////// 4 | -3 1 | -9 ////////// 5 | -6 2 | -27 ////////// 6 | -9 3 | -81 ////////// 7 | -12 4 | -243 ////////// 8 | -15 I did this to separate the charts better Use the tables to choose the correct statements. a. Table 1

  51. Math

    Explain in a variety of ways how you can distinguish the exponential function f(x)=2^x from the quadratic function f(x)=x^2 and linear function f(x)=2x. (Hint: Compare the rate of change using finite differences in table of values; identify a constant

  52. Algebra 2

    a) A population of 460 animals that increases at an annual rate of 15%. Write an exponential function to model. b) Write an exponential function to model. Predict the value of the function after 5 years(nearest whole number). A population of 430 animals

  53. math

    find an exponential function of the form P(t)yoe^kt to model the given; In 1995, the number of female athletes participating in Summer Olympics-Type Games was 550. In 1996, about 3550 participated in the summer olympics in ATlanta. Assuming that P(0)= 500

  54. Calculus

    The price-demand and cost functions for the production of microwaves are given as p=235−x40 and C(x)=14000+70x, where x is the number of microwaves that can be sold at a price of p dollars per unit and C(x) is the total cost (in dollars) of producing x

  55. Math

    State whether the equation y=10^3x represents a linear, quadratic, or exponential function. Tell how you decided. I think it is exponential

  56. algebra

    Write an exponential function to model the situation. Then predict the value of the function after 5 years (to the nearest whole number). A population of 210 animals that increases at an annual rae of 19% Can you explain your answer please?

  57. Math

    1.A scientist is studying the growth of a particular species of plant. He writes the following equation to show the height of the plant f(n), in cm, after n days: f(n) = 12(1.03)n Part A: When the scientist concluded his study, the height of the plant was

  58. Calculus

    The marginal revenue for x items in dollars is given by R′(x)=−4.5x+6. Determine (a) the revenue function and (b) the demand function. I know the revenue function is R(x)=6x-2.25x^2 just by finding the antiderivative. demand = revenue - cost, but how

  59. calculus

    Evaluating an exponential function The function gives the value of a home in dollars in the year 1980 + t. What was the value of the home in 1988? Round your answer to the nearest whole dollar amount and give units. You would evaluate for t=8. The units

  60. Helpppp Math!!!

    The market value (in thousands of dollars)of a certain home is a linear function of t, the time in years since 1990. In 1992 the market value was 68 thousand dollars, while in 1997 the market value was 79 thousand dollars -Find the slope of V as a linear

  61. Precalculus

    Suppose f is a function with exponential decay. Explain why the function g defined by g(x)=1/f(x) is a function with exponential growth. PLEASE HELP!!

  62. College Algebra

    1.Give a quadratic function q(x) with a vertex of (-1, 2). 2. Give a function h(x) which does not have an inverse function. 3. Give a polynomial function g(x) with zeros 1,2,3 4. Give an exponential function s(x) passing through (0,2) and (4,1). 5. Give a

  63. Math

    True or False. If possible kindly explain why so that I can understand it. Thanks much. 1. f(x) = 1^x is not an exponential function. 2. Every exponential function is strictly increasing.

  64. Algebra

    Describe the differences between a linear function and an exponential function. my answer is Linear functions have a constant rate of change while an exponential function has a constant finite ratio.

  65. Calculus

    Given y=log(x), what is dy/dx? If you have to derive this from first principles, then you have to use the defintion of the Logarithm. E.g. you could use that the Logarithm is the inverse of the exponential function and that the derivative of the

  66. Math

    How can you distinguish between and exponential function y =3x, from a linear function y =3x and from a quadratic function y =3x2?

  67. MATH

    State whether each equation in Exercises 25–30 represents a linear, quadratic, or exponential function. Tell how you decided. 3x^2=5 *I believe this equation is a exponential function but, I'm not sure how to explain it.*

  68. Math (Algebra)

    I am having a bit of trouble with the question stated below. I am home-schooled and learning math on your own has proven to be quite the difficult task. If someone could please explain how to do this as thoroughly as possible, I would greatly appreciate

  69. Math

    Let f(t) be an exponential function with f(0) = 11 and f(4) = 59. Use the form f(t) = Pa^t to find an equation for this exponential function? What is the Value of P and A? Thanks!

  70. calculus

    writing an exponential equation The function gives the value of a home in dollars in the year 1980 + t. Write an equation that can be used to determine the year in which the value of the home reached $100,000? Use ^ to denote an exponent. Do not solve the

  71. Math *Updated*

    So I figured out how to do the first 6, how do I do the remaining? 7. Evaluate the function below over the domain {-1, 0, 1, 2}. As the values of the domain increase, do the values of the function increase or decrease? y = (3/4)ˣ 8. Suppose an investment

  72. Algebra 2

    Given the exponential function A(x) = P(1 + r)x, what value for r will make the function a decay function? r = −2.1 r = 2.1 r = 0 r = 0.1

  73. Algebra I

    5. Holly wants to invest $1000. The table below shows the value of her investment under two different options for two different years: Part A: What type of function, linear or exponential, can be used to describe the value of the investment after a fixed

  74. math (5)

    Country Workshop manufactures both finished and unfinished furniture for the home. The estimated quantities demanded each week of its rolltop desks in the finished and unfinished versions are x and y units when the corresponding unit prices, in dollars,

  75. Math

    How would I do these? 6. The speed of sound is approximately 1.2 × 10³ km/h. How long does it take for sound to travel 7.2 × 10² km? Write your answer in minutes. 7. Evaluate the function below over the domain {-1, 0, 1, 2}. As the values of the domain

  76. Calc

    Set up an exponential function to model each real world situation. 1) A mosquito population doubles every 10 days. Two mosquitoes of the opposite sex begin the process. Function: 2 x 2^t/100 2) Given the current inflation rate (~3%), prices double every 23

  77. maths

    find any stationary points for the function h(x)=x*e^x(4-x)/6 (exponential function with e to power x *(brackets)

  78. math

    write a quadratic function and an exponential function with a base of 2 whose values at x=5 are between 50 and 64

  79. math

    a company makes and sells sailboats. The company's cost function in thousands of dollars is C(x)=2x+20, and the revenue function in thousands of dollars is R(x)=4x, where x is the number of sailboats. Find and simplify the profit function, P(x). How many

  80. MATHS

    A company is a monopolist. The demand function for its product is as follows: Q = 60 – 0.4P + 6Y + 2A Where Q = quantity sold in units P = Price per unit Y = per capita disposal income (thousands of dollars) A = hundreds of dollars of advertising

  81. Math

    What are some examples of exponential function (Using the formula: Al = A0(1/2)^t/h ), trig functions that are used to find amplitude, period, max, min etc., and combinations of transformation at home or in life in general?

  82. MATH

    Suppose you are exchanging currency in the London airport. The currency exchange service there only makes transactions in which one of the two currencies is British pounds, but you want to exchange dollars for Euros. Thus you first need to exchange dollars

  83. Algebra

    For the exponential function ex and logarithmic function log x, graphically show the effect if x is doubled. I am having trouble figuring out my points to plot on the graph.

  84. math - another ? - exponentials

    The two formulas f(t) = Pa^t and f(t) = Pe^rt provide two models for the same exponential growth or decay function. How are the exact values of a and r related? (Hint: Find a formula for a as a function of r)

  85. math

    Suppose you are exchanging currency in the London airport. The currency exchange service there only makes transactions in which one of the two currencies is British pounds, but you want to exchange dollars for Euros. Thus you first need to exchange dollars

  86. Algebra

    14. (a) Use a graphing utility to find the exponential regression function for the follow data: {(23.5, 16), (26.7, 48), (28.0, 155), (29.5, 571), (29.9, 896)} (b) Use the function in (a) to predict (to the nearest whole number) the y-value associated with

  87. economics

    HELP!!!!! One and only Inc is a monopolist. The demand function for its product is estimated to be Q=60-0.4P +6Y+2A Y=3,000 P=Price per Unit Y=Per capita disposable personal income (thousands of dollars) A=hundreds of dollars of advertising expenses The

  88. Math

    How is an exponential function different from a polynomial function? Examples?

  89. Algebra

    Construct exponential functiom of points (0,200) and (6,380). The exponential function is y(x)=____

  90. Precalculus / Statistics

    I have a question about residual plots and regression equations. The data is: X Y 1 6.1 2 5.5 3 9.8 4 10.6 5 14.2 6 21.5 7 29.9 8 37.2 9 50.6 10 64 11 77.6 What function fits this data the best, between Exponential, Linear, Quadratic, and Power. Also how

  91. Math

    State whether the equation y=10^3x represents a linear, quadratic, or exponential function. Tell how you decided. I think it is exponential, is this correct

  92. Math

    (a) Consider the improper function f(x)= (x^4+x^3+2x^2+x-1)/(x^3-x^2+x-1). Use long division to convert f(x) into a polynomial plus a proper rational function. -->I ended up with : (x+2) + (3x^2-2x-3)/(x^3-x^2+x-1) (b) Factor the polynomial Q(x) = x^3 -

  93. functions (easy explanation)

    I have a very quick question about exponential functions. I know how to use them and apply them but I don't know how to explain why they are always positive. Does anyone know why? An example of an exponential function would be 5 to the power of x. Thank

  94. math - algebra

    f(t) is an exponential function with f(0) = 200 and f(3) = 2000. a) Use the form f(t) = Pe^rt to find the equation of this exponential function. b) In the form f(x) = Pa^x, a is the growth factor. find the growth factor. c)What input value gives an output

  95. math - algebra

    f(t) is an exponential function with f(0) = 200 and f(3) = 2000. a) Use the form f(t) = Pe^rt to find the equation of this exponential function. b) In the form f(x) = Pa^x, a is the growth factor. find the growth factor. c)What input value gives an output

  96. math - algebra

    f(t) is an exponential function with f(0) = 200 and f(3) = 2000. a) Use the form f(t) = Pe^rt to find the equation of this exponential function. b) In the form f(x) = Pa^x, a is the growth factor. find the growth factor. c)What input value gives an output

  97. College Algebra

    Graph the exponential function. f(x)=4^x Clear All Draw: Exponential.

  98. algebra 1

    Gordon is evaluating some stocks he wants to purchase. You can see the function of the stock price below. The variable x represents days. Stock A B C Price f(x) = 25(1.08)x x f(x) 0 22.00 1 21.56 2 21.13 The initial price of this stock is $30, but it has

  99. Algebra 1

    Tom claims that because the data pairs (1, 4), (2, 6), (3, 9), and (4, 13.5) have y-value with a common ratio, they are best modeled by a quadratic function. What is his error? Is it supposed to be modeled by an exponential function?

  100. Math

    Given the following data set, x 0 1 2 3 4 5 6 y 0.06 0.156 0.4056 1.05456 2.741856 7.1288256 18.53494656 Determine by regression the best exponential function that fits the data Function =

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