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How does $h(x) = 10^x$ change over the interval from $x = 5$ to $x = 6$ ? $\newline$ Choices: $\newline$ (A) $h(x)$ increases by $10\%$ $\newline$ (B) $h(x)$ increases by $900\%$ $\newline$ (C) $h(x)$ increases by $10$ $\newline$ (D) $h(x)$ decreases by $10$

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Full solution

Q. How does

h(x) = 10^x

change over the interval from

x = 5

to

x = 6

?

\newline

Choices:

\newline

(A)

h(x)

increases by

10\%

\newline

(B)

h(x)

increases by

900\%

\newline

(C)

h(x)

increases by

10

\newline

(D)

h(x)

decreases by

10

Calculate $h(6)$ : Now, calculate $h(6)$ which is $10^6$ . $\newline$ $h(6) = 10^6 = 1,000,000.$
Find increase: Find the increase from $h(5)$ to $h(6)$ . $\newline$ Increase = $h(6) - h(5) = 1,000,000 - 100,000 = 900,000$ .
Determine percentage increase: Determine the percentage increase. $\newline$ Percentage increase = $(\text{Increase} / h(5)) \times 100\%$ = $(900,000 / 100,000) \times 100\%$ = $900\%$ .

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