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

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

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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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Math Problems

Algebra 2

Exponential functions over unit intervals

Full solution

Q. How does

g(x) = 5^x

change over the interval from

x = 9

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 $5$ .