Chapter 5, Problem 99RE

(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,

  $y=165.73{\left(0.955\right)}^x$

Therefore, the exponential model for the given data is $y=165.73{\left(0.955\right)}^x$ .

(c)

To determine

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

Explanation of Solution

Consider the exponential function.

  $y=165.73{\left(0.955\right)}^x$

The graph is shown in figure below.

  

Figure (2)

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

(d)

To determine

To predict :The duration required to reach temperature $110°\text{F}$ .

Explanation of Solution

Consider the exponential function.

  $y=165.73{\left(0.955\right)}^x$

Substitute $110$ for $y$ in the above expression.

  $\begin{array}{c}110=165.73{\left(0.955\right)}^x\\ x=83\sec \end{array}$

Therefore, duration required to reach temperature $110°\text{F}$ is $83\sec$