Chapter SH, Problem 5.11EP

a.

To determine

To graph the function for $0\le t\le 10$ .

Explanation of Solution

Given:

The function that models the yearly sales of cell phones,

  $s(t)=0.45t^4+5.4t^3-15t^2-300t+1000$

Calculation:

Consider the function that models the yearly sales of cell phones,

  $s(t)=0.45t^4+5.4t^3-15t^2-300t+1000$ ...... (1)

Here, s is the annual sales in millions of dollars and $t$ is the number of years after 2005.

Make a table of values for the given function as follows

Plot all these points on a graph paper and join them. The graph of given function is as follows:

  

b.

To determine

To describe the turning points of the graph and its end behavior.

Explanation of Solution

Given:

The function that models the yearly sales of cell phones,

  $s(t)=0.45t^4+5.4t^3-15t^2-300t+1000$

Calculation:

There is a relative minimum near $t=4$ . Hence, it is a turning point of the graph.

The end behavior of the graph is $s(t)\to \infty \text{ as }t\to \infty$ and $s(t)\to \infty \text{ as }t\to -\infty$ .

c.

To determine

To find out the trend in cell phones from the graph.

Explanation of Solution

Given:

The function that models the yearly sales of cell phones,

  $s(t)=0.45t^4+5.4t^3-15t^2-300t+1000$

Calculation:

The yearly sales of cell phones decreases from year 2005 to 2009. It then starts increasing from 2009.

d.

To determine

To find whether it is reasonable that the trend will continue indefinitely.

Answer to Problem 5.11EP

Unreasonable.

Explanation of Solution

Given:

The function that models the yearly sales of cell phones,

  $s(t)=0.45t^4+5.4t^3-15t^2-300t+1000$

Calculation:

This trend may continue for a number of years, but the graph will become unreasonable as the yearly sales of cell phones are increasing with high speed. So, the yearly sales will become out of control after a specific time.