Chapter 15.3, Problem 31E

a.

To determine

To sketch the graph of the function $r(t)$ for $0\le t\le 12$ .

Answer to Problem 31E

  $\text{63}\text{.6}$

Explanation of Solution

Given:

The model for the electricity bill can be modeled by the equation-

  $r(t)=50+36t-3t^2$

Calculation:

The following the graph of the model $r(t)=50+36t-3t^2$ -

  

b.

To determine

To find the total amount of the money Johnson would spend on electricity during a full year.

Answer to Problem 31E

The total money spent will be $446$ dollars.

Explanation of Solution

Given:

The model for the electricity bill can be modeled by the equation-

  $r(t)=50+36t-3t^2$ Dollars per month.

Calculation:

Substituting the value of $t=12$ in the given equation -

  $\begin{array}{l}r(t)=50+36t-3t^2\\ r(12)=50+36\times 12-3\times 12\\ r(12)=50+396\\ r(12)=446\end{array}$

Therefore the total money spent will be $446$ dollars.

c.

To determine

To find the monthly charge for Johnson.

Answer to Problem 31E

The charge will be $37.16$ dollars per month.

Explanation of Solution

Given:

The model for the electricity bill can be modeled by the equation-

  $r(t)=50+36t-3t^2$ Dollars per month.

Calculation:

The monthly charge will be

  $\frac{446}{12}=37.16$

The charge will be $37.16$ dollars per month.