Question

Write an exponential function to model the situation. A population of 470 animals decreases at an annual rate of 12%.

Answer 1

$\bf \qquad \textit{Amount for Exponential Decay} \\\\ A=P(1 - r)^t\qquad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{initial amount}\to &470\\ r=rate\to 12\%\to \frac{12}{100}\to &0.12\\ t=\textit{elapsed time}\\ \end{cases} \\\\\\ A=470(1-0.12)^t\implies A=470(0.88)^t$

Answer 2

The exponential function that models the following situation is given as follows:

$A(t) = 470(0.88)^t$

What is an exponential function?

A decaying exponential function is modeled by:

$A(t) = A(0)(1 - r)^t$

In which:

• A(0) is the initial value.

• r is the decay rate, as a decimal.

In this problem:

• The initial population is of 470 animals, hence A(0) = 470.

• It decreases 12% a year, hence r = 0.12.

Then, the equation is given by:

$A(t) = A(0)(1 - r)^t$

$A(t) = 470(1 - 0.12)^t$

$A(t) = 470(0.88)^t$

More can be learned about exponential functions at https://brainly.com/question/25537936

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