1. The function f(x) = 5(1.24)x models the length (cm) of a lizard from the beginning of a lizard's life. According to the model, which represents the growth factor throughout the lizard's life?
A) 1.24 ***
B) 5
C) x
D) y
2. The distance from Jim's house to the intersection of Thornwood Drive and Holly Drive is given by the expression 15x − 7. The total distance from Jim's house to Adam's house when traveled on Thornwood Drive and Holly Drive is given by the expression 23x − 2. Find a single expression that represents the distance from Adam's house to the intersection of Thornwood Drive and Holly Drive.
A) 8x + 5
B) 8x − 9
C) 38x + 5
D) 38x − 9***
Which polynomial is in standard form?
A) 2x + 3x3 + 5x5 + 9x4 + 2x
B) 5 + 3x + x2 + 2x4 + 2x5 ***
C) 8x7 + 3x6 + x5 + 5x4 − 2x3
D) 8x2 + 3x5 + x6 + 5x7 − 2
#1 ok
#2 nope. You want to subtract. Read the question again, and draw and label a diagram if necessary.
#3 nope. Time to review the standard form.
And use ^ for exponents.
x^2, or 1.24^x
The table shows the behavior of a quadratic and an exponential function near the origin.
A. Which function is growing more rapidly?
B. Between which x-values does the table indicate that the functions' graphs have crossed?
C. Will the functions' graphs ever intersect again? Can you prove this?
1. The growth factor throughout the lizard's life is represented by the value in the exponent of the function. In this case, the growth factor is 1.24 because it is the value of x in the function f(x) = 5(1.24)x.
2. To find the distance from Adam's house to the intersection of Thornwood Drive and Holly Drive, we need to subtract the distance from Jim's house to the intersection from the total distance from Jim's house to Adam's house. So the expression representing the distance from Adam's house to the intersection is:
(23x - 2) - (15x - 7) = 23x - 2 - 15x + 7 = 8x + 5. Therefore, the correct answer is A) 8x + 5.
3. A polynomial is in standard form when the terms are written in descending order of degree (highest degree first) and the coefficients are written in standard numerical order. In this case, the polynomial that is in standard form is B) 5 + 3x + x^2 + 2x^4 + 2x^5.
1. To find the growth factor in the function f(x) = 5(1.24)^x, we look for the numerical value that is being raised to the power of x. In this case, it is 1.24. Therefore, the growth factor throughout the lizard's life is 1.24.
2. To find the distance from Adam's house to the intersection of Thornwood Drive and Holly Drive, we need to subtract Jim's distance from the total distance. The expression for Jim's distance is 15x - 7, and the expression for the total distance is 23x - 2. Therefore, the expression for Adam's distance is (23x - 2) - (15x - 7), which simplifies to 23x - 2 - 15x + 7. Combining like terms, we get 8x + 5.
3. Standard form for a polynomial is when the terms are arranged from highest to lowest degree. In the given options, the polynomial in standard form is B) 5 + 3x + x^2 + 2x^4 + 2x^5. The terms are arranged in increasing order of degree, starting from degree 0 (constant term) and ending with the highest degree term.