Chapter 1.7, Problem 45PPS

(a)

To determine

To graph: The function $f\left(t\right)=0.8t+72$ .

Explanation of Solution

Given information:

The function is $f\left(t\right)=0.8t+72$ .

Graph:

The graph of the function $f\left(t\right)=0.8t+72$ is shown below.

  

Figure (1)

Interpretation:

In the graph, the line passes through the points $\left(-90,0\right)$ and $\left(0,72\right)$ .

(b)

To determine

To find: The science score that corresponds to a math score of $308$ .

Answer to Problem 45PPS

The science score is $295$ .

Explanation of Solution

Given information:

The function is $f\left(t\right)=0.8t+72$ and math score is $308$ .

Calculation:

Substitute $308$ for $f\left(t\right)$ in the function $f\left(t\right)=0.8t+72$ .

  $\begin{array}{c}308=0.8t+72\\ 0.8t=308-72\\ t=\frac{236}{0.8}\\ =295\end{array}$

Therefore, the science score is $295$ .

(c)

To determine

To describe: The domain and range of the data.

Answer to Problem 45PPS

The domain is the set of science score that is $\left\{295\right\}$ and the range is set of math score that is $\left\{308\right\}$ .

Explanation of Solution

Given information:

The function is $f\left(t\right)=0.8t+72$ .

Calculation:

The $t$ value will be the domain and $f\left(t\right)$ values will be the range of the data.

The domain is the set of science score that is $\left\{295\right\}$ and the range is set of math score that is $\left\{308\right\}$ .