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How does $h(x) = 5^x$ change over the interval from $x = 2$ to $x = 3$ ? $\newline$ Choices: $\newline$ $h(x)$ increases by 200% $\newline$ $h(x)$ increases by a factor of 25 $\newline$ $h(x)$ decreases by 60% $\newline$ $h(x)$ increases by a factor of 5

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Identify independent and dependent variables

Full solution

Q. How does

h(x) = 5^x

change over the interval from

x = 2

to

x = 3

?

\newline

Choices:

\newline

h(x)

increases by 200%

\newline

h(x)

increases by a factor of 25

\newline

h(x)

decreases by 60%

\newline

h(x)

increases by a factor of 5

Calculate h( $2$ ): First, calculate $h(2)$ . $\newline$ $h(2) = 5^2 = 25$
Calculate h( $3$ ): Next, calculate $h(3)$ . $\newline$ $h(3) = 5^3 = 125$
Find Change: Find the change in $h(x)$ from $x = 2$ to $x = 3$ . $\newline$ Change = $h(3) - h(2) = 125 - 25 = 100$
Determine Factor: Determine the factor of increase. $\newline$ Factor of increase = $\frac{h(3)}{h(2)} = \frac{125}{25} = 5$
Check Choices: Check the choices to see which one matches the factor of increase. $\newline$ The correct choice is: $h(x)$ increases by a factor of $5$ .

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