Chapter 5, Problem 101RE

(a)

To determine

To draw:The scatter diagram for the data.

Explanation of Solution

The scatter diagram for the data is shown in figure below.

  

Figure (1)

Therefore, the scatter diagram for the data is shown in Figure (1)

(b)

To determine

To build:The exponential model for the given data.

Explanation of Solution

The scatter diagram for the data is shown in figure below.

  

The exponential model for the given data is,

  $y=\frac{46.92}{1+21.27e^{-0.73x}}$

Therefore, the exponential model for the given data is $y=\frac{46.92}{1+21.27e^{-0.73x}}$ .

(c)

To determine

To graph :The exponential function obtained in part (b).

Explanation of Solution

Consider the exponential function.

  $y=\frac{46.92}{1+21.27e^{-0.73x}}$

The graph is shown in figure below.

  

Figure (2)

Therefore, the graph of exponential model is shown in Figure (2).

(d)

To determine

To find:The maximum number of people who will catch cold.

Explanation of Solution

Consider the exponential function.

  $y=\frac{46.92}{1+21.27e^{-0.73x}}$

The maximum number of people who will catch the cold is,

  $\begin{array}{c}y=\frac{46.92}{1+21.27e^{-0.73\left(\infty \right)}}\\ =\frac{46.92}{1+0}\\ =46.92\\ \approx 47\end{array}$

Therefore, maximum number of people who will catch the cold is $47$ .

(e)

To determine

To find:The duration when 10 people died.

Explanation of Solution

Consider the exponential function.

  $y=\frac{46.92}{1+21.27e^{-0.73x}}$

Substitute $10$ for $y$ in the above expression.

  $\begin{array}{c}10=\frac{46.92}{1+21.27e^{-0.73\left(s\right)}}\\ x=2.39\text{days}\\ \approx \text{3}\text{days}\end{array}$

Therefore, the duration when 10 people died is $3$ days.

(f)

To determine

To find:The duration when it will take for $46$ people to catch cold.

Explanation of Solution

Consider the exponential function.

  $y=\frac{46.92}{1+21.27e^{-0.73x}}$

Substitute $46$ for $y$ in the above expression.

  $\begin{array}{c}46=\frac{46.92}{1+21.27e^{-0.73\left(x\right)}}\\ x=9.54\text{days}\\ \approx \text{10}\text{days}\end{array}$

Therefore, the duration when 46 people will catch cod is $10$ days.