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How does $g(t) = 7^t$ change over the interval from $t = 5$ to $t = 6$ ? $\newline$ Choices: $\newline$ (A) $g(t)$ decreases by $7\%$ $\newline$ (B) $g(t)$ increases by $7$ $\newline$ (C) $g(t)$ increases by $7\%$ $\newline$ (D) $g(t)$ increases by a factor of $7$

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Exponential functions over unit intervals

Full solution

Q. How does

g(t) = 7^t

change over the interval from

t = 5

to

t = 6

?

\newline

Choices:

\newline

(A)

g(t)

decreases by

7\%

\newline

(B)

g(t)

increases by

7

\newline

(C)

g(t)

increases by

7\%

\newline

(D)

g(t)

increases by a factor of

7

Calculate $g(5)$ : Calculate $g(5)$ by plugging in $t = 5$ into the function. $\newline$ $g(5) = 7^5$
Calculate $g(6)$ : Calculate $g(6)$ by plugging in $t = 6$ into the function. $\newline$ $g(6) = 7^6$
Find factor of increase: Find the factor of increase from $g(5)$ to $g(6)$ . $\newline$ Factor of increase = $\frac{g(6)}{g(5)} = \frac{7^6}{7^5}$
Simplify factor of increase: Simplify the factor of increase. $\newline$ Factor of increase = $7^{(6-5)} = 7^1 = 7$
Determine correct choice: Determine the correct choice based on the factor of increase. $\newline$ Since $g(t)$ increases by a factor of $7$ , the correct choice is (D) $g(t)$ increases by a factor of $7$ .

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