Question

This is not from a test or graded assessment.The first drop down menu the choices are: 370, 322, or 209. The second drop down menu: Growth or decay. The third drop down menu: 1.075, 92.5 9.25, 7.5

Answer 1

Given that the following Exponential Function represents the population size of a certain species of birds in a park after "t" years:

$P(t)=322(1.075)^t$

You need to remember that an Exponential Function has this form:

$f(x)=a\cdot b^x$

Where "a" is the initial value, and it is an Exponential Gwroth when the base "b" is:

$b>1$

In this case, you can identify that:

$\begin{gathered} a=322 \\ b=1.075 \end{gathered}$

Since:

$1.075>1$

It represents growth.

By definition, for an Exponential Growth:

$b=1+r$

Where "r" is the rate of growth (expressed in decimal form).

In this case, you can determine that:

$\begin{gathered} r=b-1 \\ r=1.075-1 \\ r=0.075 \end{gathered}$

In order to convert it to a percentage, you need to multiply the decimal number by 100:

$0.075\cdot100=7.5$

Hence, the answers are:

• Initial population size:

$322$

• Growth.

,

• Percentage:

$7.5\text{\%}$