Question

A satellite dish company charges a one-time installation of of $75 and then a monthly usage charge of $40. The total cost C using that satellite is given by the function C(t) = 40t + 75, where T is the time (in months) since starting the service. For the situation given below, describe the new function using the graph of C(t) = 40t + 75 as a reference.

a. The satellite dish company reduces its one-time installation fee to $60. What change would you make to the graph of C(t) = 40t + 75 to obtain the new graph?

b. The satellite dish company decreases its monthly fee to $30. What change would you make to the graph C(t) = 40t +75 to obtain the new graph?

c. What is the new function with both changes?

Answer 1

Functions can be represented using equations.

• Change 75 to 60
• Change 40 to 30
• The new functions are $\mathbf{C(t) = 40t + 60}$ and $\mathbf{C(t) = 30t + 75}$

The function is given as:

$\mathbf{C(t) = 40t + 75}$

(a) The one-time installation fee is to be changed to $60

A linear function is represented as:

$\mathbf{y = mx + b}$

In this context, b represents the one-time installation fee.

So, by comparison:

$\mathbf{b = 75}$

So, in the new function;

The value of b would be:

$\mathbf{b = 60}$

(b) The monthly fee is to be reduced to $30 per month

A linear function is represented as:

$\mathbf{y = mx + b}$

In this context, m represents the monthly fee

So, by comparison:

$\mathbf{m = 40}$

So, in the new function;

The value of m would be:

$\mathbf{m = 30}$

(c) The new functions

In (a), we have:

$\mathbf{b = 60}$

So, the new function is:

$\mathbf{C(t) = 40t + 60}$

In (b), we have:

$\mathbf{m = 30}$

So, the new function is:

$\mathbf{C(t) = 30t + 75}$

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