How does g(x) = 7^x change over the interval from x = 3 to x = 4? Choices: [[g(x) increases by a factor of 7][g(x) increases by a factor of 21][g(x) increases by 200%][g(x) decreases by a factor of 7]]

Find g(3): Find g(3). g(3) = 7^3 g(3) = 343Find g(4): Find g(4). g(4) = 7^4 g(4) = 2401Calculate percentage change: Calculate the percentage change from x = 3 to x = 4. % change = [(2401 - 343) / 343] * 100% % change = [2058 / 343] * 100% % change ≈ 600%Check factor increase: Check if g(x) increases by a factor of 7. Factor = g(4) / g(3) Factor = 2401 / 343 Factor = 7

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How does $g(x) = 7^x$ change over the interval from $x = 3$ to $x = 4$ ? $\newline$ Choices: $\newline$ $g(x)$ increases by a factor of $7$ $\newline$ $g(x)$ increases by a factor of $21$ $\newline$ $g(x)$ increases by $200\%$ $\newline$ $g(x)$ decreases by a factor of $7$

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Math Problems

Algebra 2

Exponential functions over unit intervals

Full solution

Q. How does

g(x) = 7^x

change over the interval from

x = 3

x = 4

\newline

Choices:

\newline

g(x)

increases by a factor of

7

\newline

g(x)

increases by a factor of

21

\newline

g(x)

increases by

200\%

\newline

g(x)

decreases by a factor of

7

Find $g(3)$ : Find $g(3)$ . $g(3) = 7^3$ $g(3) = 343$
Find $g(4)$ : Find $g(4)$ . $g(4) = 7^4$ $g(4) = 2401$
Calculate percentage change: Calculate the percentage change from $x = 3$ to $x = 4$ . % change = $\left( \frac{2401 - 343}{343} \right) \times 100\%$ % change = $\left( \frac{2058}{343} \right) \times 100\%$ % change \approx $600$ \%
Check factor increase: Check if $g(x)$ increases by a factor of $7$ .
Factor = $\frac{g(4)}{g(3)}$
Factor = $\frac{2401}{343}$
Factor = $7$