# 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.

1. 👍
2. 👎
3. 👁
1. You know that y=e^x goes through (0,1) and has an asymptote at y=0, so,
y = e^x + 3 has its asymptote at y=3.
Further, 5e^x goes through (0,5), so one function would be

5e^x + 3

Now, you can pick any number greater than 1, and the above statements hold true, so

5*2^x, 5*10^x all do the same.

In fact, that also means that

5*12^7x, 5*1.001^100x all do it to.

Since a*b^(kx) = a*e^((k lnb) x)

1. 👍
2. 👎
2. This is incorrect

1. 👍
2. 👎

## Similar Questions

1. ### 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

2. ### Math

1. Does the table represent an exponential function? X: 1, 2, 3, 4 Y:-1,-8,-27,-64 Yes or No? I am confused on this, so help would be nice. Thank you.

3. ### Mathematics

For question 1 & 2, find the x- and y-intercept of the line. 1. -10x + 5y = 40 A. x-intercept is 5; y-intercept is -10 B. x-intercept is 8; y-intercept is -4 C. x-intercept is -10; y-intercept is 5 D. x-intercept is -4;

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) = 8(1.05)n Part A: When the scientist concluded his study, the

1. ### math

This is for the pretest. What is the solution to the system of equations pictured below? A.(-3,5) B.(-3,-2) C(3,4) D.(1,2) E(6,-2) When writing in slope intercept form what does the 'm" Represent? What is the 'b'? A. M is the x

2. ### Algebra2

Determine whether the function represents exponential growth or decay. Then find the y-intercept. y=4(5/6)^x

3. ### math

Austin is creating a new trail mix by combining two of his best­selling blends. A pineapple­coconut­macadamia (pcm) mix that sells for \$18/kg and a banana­papayapeanut (bpp) mix that sells for \$10/kg. Write the equations and

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

1. ### MATH

1. Does the table represent an exponential function? Does the table represent an exponential function? X 1,2,3,4 Y -1,-8,-27,-64 yes? no?

2. ### Algebra

a. Do some research and find a city that has experienced population growth. Determine its population on January 1st of a certain year. Write an exponential function to represent the city’s population, y, based on the number of

3. ### 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

4. ### Math

Write an equation to represent a rational function with the following conditions: - reciprocal of a quadratic function - asymptotes with the equations x = -5, x= 4/3, and y = 0 - y < 0 whenever x < -5 - y-intercept of 1.5