How does h(x) = 8^x change over the interval from x = 3 to x = 4? Choices: (A)h(x) increases by a factor of 8 (B)h(x) decreases by 8% (C)h(x) increases by 8 (D)h(x) increases by 8%

Calculate h(3): Calculate h(3) by substituting x = 3 into h(x) = 8^x. h(3) = 8^3 h(3) = 512Calculate h(4): Now calculate h(4) by substituting x = 4 into h(x) = 8^x. h(4) = 8^4 h(4) = 4096Compare h(3) and h(4): Compare h(3) and h(4) to determine the change. h(3) = 512 and h(4) = 4096, so h(x) increases.Calculate factor increase: Calculate the factor by which h(x) increases from x = 3 to x = 4. Factor increase = h(4) / h(3) Factor increase = 4096 / 512 Factor increase = 8Match calculated factor increase: Determine which choice matches the calculated factor increase. The correct choice is (A) h(x) increases by a factor of 8.

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How does $h(x) = 8^x$ change over the interval from $x = 3$ to $x = 4$ ? $\newline$ Choices: $\newline$ (A) $h(x)$ increases by a factor of $8$ $\newline$ (B) $h(x)$ decreases by $8\%$ $\newline$ (C) $h(x)$ increases by $8$ $\newline$ (D) $h(x)$ increases by $8\%$

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Math Problems

Algebra 2

Exponential functions over unit intervals

Full solution

Q. How does

h(x) = 8^x

change over the interval from

x = 3

x = 4

\newline

Choices:

\newline

(A)

h(x)

increases by a factor of

8

\newline

(B)

h(x)

decreases by

8\%

\newline

(C)

h(x)

increases by

8

\newline

(D)

h(x)

increases by

8\%

Calculate $h(3)$ : Calculate $h(3)$ by substituting $x = 3$ into $h(x) = 8^x$ . $\newline$ $h(3) = 8^3$ $\newline$ $h(3) = 512$
Calculate $h(4)$ : Now calculate $h(4)$ by substituting $x = 4$ into $h(x) = 8^x$ .
$h(4) = 8^4$
$h(4) = 4096$
Compare $h(3)$ and $h(4)$ : Compare $h(3)$ and $h(4)$ to determine the change. $\newline$ $h(3) = 512$ and $h(4) = 4096$ , so $h(x)$ increases.
Calculate factor increase: Calculate the factor by which $h(x)$ increases from $x = 3$ to $x = 4$ .
Factor increase = $\frac{h(4)}{h(3)}$
Factor increase = $\frac{4096}{512}$
Factor increase = $8$
Match calculated factor increase: Determine which choice matches the calculated factor increase. The correct choice is (A) $h(x)$ increases by a factor of $8$ .