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Question

A cell phone company charges $60 for a cell phone and $40 per month under its economy plan. Formulate and graph a model that can be used to determine the total cost, C(t), of operating a cell phone for t months. Find the total cost for 5 and 1/2 months of service and the domain of C.

I understand everything except how you would find the domain of C. Please walk me through it so I can apply it to other problems. Thank you so much!

Answer 1

did you have C(t) = 40t + 60 ?

now the graph would only make physical sense for the part in the first quadrant.

the y-intercept is the point (0,60), (even with no calls you would pay $60)

the graph would continue to rise as t increases.
so the lowest Cost is 60 and there is really no upper limit, but we have to be reasonable about large values of t
e.g. if t = 1000, this would make no sense because 1000 months from now, cells phones may only be found in museums.

I would say the domain of t is any reasonable value of t , t > 0

you said "domain of C", what you meant is the range of C

domain deals with the horizontal variable,
range deals with the vertical variable of your function.

Answer 2

That's funny, because in my packet, it said to "find the domain of C." But I see how that would not make sense.

Thanks!