Question

A cellular service provider charged a customer $40 for 150 minutes of airtime. The same provider charged another customer $55 for 300 minutes of airtime. Which linear model represents the total cost, C, as a function of t, the amount of airtime in minutes?

Answer 1

`C(t)=0.1t+25`

Step-by-step explanation:

So, we are looking for a linear equation. As we know Equation of a line has different forms, let´s use slope-intercept form:

`C(t)=mt+b`

Where C is the total cost as a function of t, t is the amount of airtime in minutes, m is the slope and b is the y-intercept

Now, let´s use the data provide in order to find m and b:

`40=150m+b` (E1)

`55=300m+b` (E2)

We have a 2X2 system of equations, let´s solve it using elimination method:

`2(E1)-(E2)`

`25=0+b\\b=25`

Replacing b in (E1) or (E2):

`m=(40-25)/(150)`

`m=(1)/(10)=0.1`

Knowing the slope m and the y-intercept b the linear model that represents the total cost as a function of t is:

`C(t)=0.1t+25`

You can check the results evaluating t=150 and t=300, the results must be 40 and 55 respectively