Chapter 4.1, Problem 36PS

Solution

a.

To find: The initial amount, growth factor, and the annual percent increase.

The initial amount is 2500 referrals.

The growth factor is 1.50.

The annual percent increase is 50%.

Given:

  $y=2500{\left(1.50\right)}^t$

Calculation:

Consider,

  $y=2500{\left(1.50\right)}^t$

It can be written as,

  $y=2500{\left(1+0.50\right)}^t$

Now by comparing with $y=a{\left(1+r\right)}^t$ , it follows that

  $a=2500,r=0.50$ .

Now the initial amount is,

  $a=2500$ referrals.

The growth factor is,

  $\begin{array}{c}1+r=1+0.50\\ =1.50\end{array}$

And the annual percent increase is,

  $\begin{array}{c}r=0.50\times 100\\ =50\%\end{array}$

b.

To graph: The given function and to find the number of referrals received in March of 2002.

  

The domain is $\left[0,5\right]$ and the range is $\left[2500,18985\right]$ .

The number of referrals received in March of 2002 is 12656.

Given:

  $y=2500{\left(1.50\right)}^t$

Calculation:

The given function passes through the points $\left(0,2500\right),\left(1,3750\right)$ .

Now the graph is,

  

The domain is $\left[0,5\right]$ and the range is $\left[2500,18985\right]$ .

From the graph, it can be seen that the number of referrals 4 years after 1998 is approximately 12656.

Hence, the number of referrals received in March of 2002 is 12656.