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How does $g(t) = 2^t$ change over the interval from $t = 7$ to $t = 8$ ? $\newline$ Choices: $\newline$ (A) $g(t)$ increases by $200\%$ $\newline$ (B) $g(t)$ decreases by a factor of $2$ $\newline$ (C) $g(t)$ increases by a factor of $2$ $\newline$ (D) $g(t)$ increases by $t = 7$ $0$

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Find derivatives of logarithmic functions

Full solution

Q. How does

g(t) = 2^t

change over the interval from

t = 7

to

t = 8

?

\newline

Choices:

\newline

(A)

g(t)

increases by

200\%

\newline

(B)

g(t)

decreases by a factor of

2

\newline

(C)

g(t)

increases by a factor of

2

\newline

(D)

g(t)

increases by

t = 7

0

Calculate $g(7)$ : Calculate $g(7)$ to find the value of the function at $t = 7$ . $\newline$ $g(7) = 2^7$ $\newline$ $g(7) = 128$
Calculate $g(8)$ : Calculate $g(8)$ to find the value of the function at $t = 8$ . $\newline$ $g(8) = 2^8$ $\newline$ $g(8) = 256$
Find factor increase: Find the factor by which $g(t)$ increases from $t = 7$ to $t = 8$ .
Factor = $\frac{g(8)}{g(7)}$
Factor = $\frac{256}{128}$
Factor = $2$
Compare factor to choices: Compare the factor of increase to the given choices. $\newline$ The factor of increase is $2$ , which corresponds to the function doubling.

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