Chapter 8.7, Problem 10E

To determine

To write:

An equation using function notation that gives the monthly cable cost of basic cable TV as a function of t .

Answer to Problem 10E

The function $f(t)=0.1125t+9.73$ gives the monthly cable cost of basic cable TV.

Explanation of Solution

Given:

The monthly average cost of basic cable TV was $9.73 in 1985 and has increased by about $1.35 each year since then.

Concepts used:

The equation of a line in slope-intercept form is $y=mx+b$ , where m represents slope of line and b represents the y -intercept.

Calculation:

Let t represent the number of years since 1985.

We know that one year equals 12 months, so the number of months in terms of t would be $\frac{t}{12}$ .

We have been given one point on a line $(0,9.73)$ and slope of line is 1.35.

To write our function, we will substitute the value of slope and the y -intercept $(0,9.73)$ in slope-intercept form of equation as shown below:

  $\begin{array}{l}y=mx+b\left(\text{Slope-intercept form of equation}\right)\\ y=1.35\cdot \frac{t}{12}+9.73\left(\text{Substituting }m=1.35\text{ and }b=9.73\right)\\ y=0.1125t+9.73\left(\text{Upon simplifying}\right)\\ f(t)=0.1125t+9.73\left(\text{Writing in function form}\right)\end{array}$

Therefore, the function $f(t)=0.1125t+9.73$ gives the monthly cable cost of basic cable TV.