Chapter 11.3, Problem 12E

(a)

To determine

To find: The number of people those who heard about the opening of the new grocery store

Within 24 hours of the announcement.

Answer to Problem 12E

The number of people heard is $211$ .

Explanation of Solution

Given:

The model for the information spread is $y=525\left(1-e^{-0.038t}\right)$ .

The number of people in the town is $525$ .

The time passed for the announcement is 24 hours.

Calculation:

Consider the given model is,

  $y=525\left(1-e^{-0.038}\right)$

Then,

  $\begin{array}{c}y=525\left(1-e^{-0.038\left(24\right)}\right)\\ =525\times 0.40172\\ =211\end{array}$

Thus, the number of people heard is $211$ .

(b)

To determine

To find: The graph of the function on the graphing calculator when the 90% of the people have heard about the grocery store opening.

Answer to Problem 12E

The required graph is shown in Figure 4 and the graph shows that after 60.5 hours around 90% of the people are informed.

Explanation of Solution

By the use graphing utility press Y= and enter the model in the calculator as shown in Figure 1

  

Figure 1

Press the window button and input the parameters as shown in Figure 2

  

Figure 2

The graph for the given model is shown in Figure 3 and is obtained by pressing the graph button.

  

Figure 3

Press the graph button trace a point on the graph as the 90% of 525 is 472.5 then trace this values as shown in Figure 4

  

Figure 4

Thus, the required graph is shown in Figure 4 and the graph shows that after 60.5 hours around 90% of the people are informed.