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hodyreva [135]
3 years ago
13

A cellular service provider charged a customer $40 for 150 minutes of airtime. The same provider charged another customer $55 fo

r 300 minutes of airtime. Which linear model represents the total cost, C, as a function of t, the amount of airtime in minutes?
Business
1 answer:
yKpoI14uk [10]3 years ago
6 0

Answer:

C(t)=0.1t+25

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=\frac{40-25}{150}

m=\frac{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

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swat32

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