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How does $f(t) = 9^t$ change over the interval from $t = 7$ to $t = 8$ ? $\newline$ Choices: $\newline$ (A) $f(t)$ increases by a factor of $9$ $\newline$ (B) $f(t)$ decreases by a factor of $9$ $\newline$ (C) $f(t)$ decreases by $9$ $\newline$ (D) $f(t)$ increases by $9$

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Find derivatives of logarithmic functions

Full solution

Q. How does

f(t) = 9^t

change over the interval from

t = 7

to

t = 8

?

\newline

Choices:

\newline

(A)

f(t)

increases by a factor of

9

\newline

(B)

f(t)

decreases by a factor of

9

\newline

(C)

f(t)

decreases by

9

\newline

(D)

f(t)

increases by

9

Calculate $f(t)$ : Calculate $f(t)$ at $t = 7$ . $\newline$ $f(7) = 9^7$
Calculate $f(t)$ : Calculate $f(t)$ at $t = 8$ . $\newline$ $f(8) = 9^8$
Find factor change: Find the factor by which $f(t)$ changes from $t = 7$ to $t = 8$ . $\newline$ Factor = $\frac{f(8)}{f(7)} = \frac{9^8}{9^7}$
Simplify expression: Simplify the expression. $\newline$ Factor = $9^{8-7} = 9^1 = 9$
Determine answer choice: Determine the correct answer choice. $\newline$ Since $f(t)$ increases by a factor of $9$ , the correct answer is (A) $f(t)$ increases by a factor of $9$ .

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