Chapter 4.1, Problem 35PS

Solution

a.

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

The initial amount is 0.42 millions.

The growth factor is 2.47.

The annual percent increase is 147%.

Given:

  $n=0.42{\left(2.47\right)}^t$

Calculation:

Consider,

  $n=0.42{\left(2.47\right)}^t$

It can be written as,

  $n=0.42{\left(1+1.47\right)}^t$

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

  $a=0.42,r=1.47$ .

Now the initial amount is,

  $a=0.42$ millions.

The growth factor is,

  $\begin{array}{c}1+r=1+1.47\\ =2.47\end{array}$

And the annual percent increase is,

  $\begin{array}{c}r=1.47\times 100\\ =147\%\end{array}$

b.

To find: The number of DVD players sold in the year 2001 by using the graph of the given function.

15.633 million DVD players sold in the year 2001.

Given:

  $n=0.42{\left(2.47\right)}^t$

Calculation:

The given function passes through the points $\left(0,0.42\right)$ , $\left(1,1.0374\right)$ .

Now the graph is,

  

From the graph, it can be seen that the number of DVD players sold 4 years after 1997 is 15.633 millions.

Hence, 15.633 million DVD players sold in the year 2001.