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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!

  • Algebra -

    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.

  • Algebra -

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


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