Answer:
[tex]C(t)=0.1t+25[/tex]
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:
[tex]C(t)=mt+b[/tex]
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:
[tex]40=150m+b[/tex] (E1)
[tex]55=300m+b[/tex] (E2)
We have a 2X2 system of equations, let´s solve it using elimination method:
[tex]2(E1)-(E2)[/tex]
[tex]25=0+b\\b=25[/tex]
Replacing b in (E1) or (E2):
[tex]m=\frac{40-25}{150}[/tex]
[tex]m=\frac{1}{10}=0.1[/tex]
Knowing the slope m and the y-intercept b the linear model that represents the total cost as a function of t is:
[tex]C(t)=0.1t+25[/tex]
You can check the results evaluating t=150 and t=300, the results must be 40 and 55 respectively
