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How does $g(x) = 5^x$ change over the interval from $x = 9$ to $x = 10$ ? $\newline$ Choices: $\newline$ (A) $g(x)$ increases by $5$ $\newline$ (B) $g(x)$ increases by a factor of $5$ $\newline$ (C) $g(x)$ decreases by a factor of $5$ $\newline$ (D) $g(x)$ increases by $x = 9$ $0$

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Exponential functions over unit intervals

Full solution

Q. How does

g(x) = 5^x

change over the interval from

x = 9

to

x = 10

?

\newline

Choices:

\newline

(A)

g(x)

increases by

5

\newline

(B)

g(x)

increases by a factor of

5

\newline

(C)

g(x)

decreases by a factor of

5

\newline

(D)

g(x)

increases by

x = 9

0

Calculate $g(9)$ : Calculate $g(9)$ by substituting $x = 9$ into $g(x) = 5^x$ . $\newline$ $g(9) = 5^9$
Calculate $g(10)$ : Calculate $g(10)$ by substituting $x = 10$ into $g(x) = 5^x$ . $\newline$ $g(10) = 5^{10}$
Compare $g(9)$ and $g(10)$ : Compare $g(9)$ and $g(10)$ to determine the change. $\newline$ Since $5^{10}$ is $5$ times larger than $5^{9}$ , $g(x)$ increases by a factor of $5$ from $x = 9$ to $g(10)$ $0$ .
Choose the correct answer: Choose the correct answer from the given choices. $\newline$ The correct choice is (B) $g(x)$ increases by a factor of $5$ .

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