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How does $h(t) = 8^t$ change over the interval from $t = 8$ to $t = 9$ ? $\newline$ Choices: $\newline$ (A) $h(t)$ increases by a factor of $8$ $\newline$ (B) $h(t)$ decreases by $8$ $\newline$ (C) $h(t)$ increases by $800\%$ $\newline$ (D) $h(t)$ increases by $8$

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Exponential functions over unit intervals

Full solution

Q. How does

h(t) = 8^t

change over the interval from

t = 8

to

t = 9

?

\newline

Choices:

\newline

(A)

h(t)

increases by a factor of

8

\newline

(B)

h(t)

decreases by

8

\newline

(C)

h(t)

increases by

800\%

\newline

(D)

h(t)

increases by

8

Calculate $h(8)$ : Calculate $h(8)$ by substituting $t = 8$ into $h(t) = 8^t$ . $\newline$ $h(8) = 8^8$
Calculate $h(9)$ : Calculate $h(9)$ by substituting $t = 9$ into $h(t) = 8^t$ . $\newline$ $h(9) = 8^9$
Compare $h(8)$ and $h(9)$ : Compare $h(8)$ and $h(9)$ to determine if $h(t)$ increases or decreases. $\newline$ Since $8^9$ is greater than $8^8$ , $h(t)$ increases.
Calculate factor of increase: Calculate the factor by which $h(t)$ increases from $t = 8$ to $t = 9$ . $\newline$ Factor = $\frac{h(9)}{h(8)} = \frac{8^9}{8^8} = 8^{9-8} = 8$
Determine percentage increase: Determine the percentage increase from $h(8)$ to $h(9)$ . $\newline$ Percentage increase = (Factor - $1$ ) * $100$ \% = ( $8$ - $1$ ) * $100$ \% = $7$ * $100$ \% = $700$ \%

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