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# Exponential Functions

## Exponential Functions 1.12 - Solution

a

Let's determine the base of the function. $\begin{gathered} y=200({\color{#FF0000}{0.75}})^t \end{gathered}$ Its base is ${\color{#FF0000}{0.75}}$ which is greater than $0$ and less than $1.$ Therefore, the model represents exponential decay.

b
We will first analyze the exponential decay model. $\begin{gathered} \underline{\textbf{Exponential Decay Model}}\\ y=\textcolor{darkorange}{a}(1-\textcolor{magenta}{r})^t \end{gathered}$ In the model, $\textcolor{darkorange}{a}$ is the initial amount and $\textcolor{magenta}{r}$ is the percent decrease written as a decimal. Knowing that the base of the function is $0.75,$ we can identify the annual percent decrease.
$1-r=0.75$
$\text{-} r=\text{-} 0.25$
$r=0.25$
$r=25\, \%$
Therefore, the annual percent decrease is $25 \, \%.$