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Math Help - rate of change word problem

  1. #1
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    rate of change word problem

    The number of subscribers to a new cable TV company t months after the opening of the business is given by s(t) = 1,500t/(t + 3)^2
    After one month in business, at what rate is the number of subscribers changing?
    A) increase of 47 subscribers/month
    B) increase of 750 subscribers/month
    C) increase of 70 subscribers/month
    D) decrease of 47 subscribers/month

    Im not sure how to do this. what I did was plug in 1 for t and I got 93.75. When I plugged in 2, I got 120. Am I supposed to find the rate of change between these numbers??
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    Re: rate of change word problem

    "After the first month" bothers me. It is not clear. All of the months, except the first, is "after the first month". If it had said "during" the first month, then I would take the number of subscribers at t= 0, 0, and at t= 1, 93.75, observe that that is a total change of 93.75 and, because that happened during one month, the "rate of change" would be 93.75 subscribers divided by 1 month= 93.75 subscribers per month.

    But you my be right that "after the first month" means "during the second month". After the first month there were 93.75 subscribers and after the second month there were 120. So during that month the number of subscribers increased by 120- 93.75= 26.25. Since that was over one month, the rate of increase is 26.25/1= 26.25 subscribers per month.

    Yet another interpretation of "after the first month" would be "all the months given after the first". That is, after the first month there were 93.75 subscribers. After t th month, there are 1500t/(t+3)^3. Subtract those to find the total change and divide by t- 1.

    Finally, since this is a Calculus problem, the instantaneous rate of change is given by the derivative. Can you find the derivative of 1500t/(t+3)^3?
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  3. #3
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    Re: rate of change word problem

    Quote Originally Posted by salma View Post
    The number of subscribers to a new cable TV company t months after the opening of the business is given by s(t) = 1,500t/(t + 3)^2
    After one month in business, at what rate is the number of subscribers changing?
    A) increase of 47 subscribers/month
    B) increase of 750 subscribers/month
    C) increase of 70 subscribers/month
    D) decrease of 47 subscribers/month

    Im not sure how to do this. what I did was plug in 1 for t and I got 93.75. When I plugged in 2, I got 120. Am I supposed to find the rate of change between these numbers??
    the question is asking for s'(1) , the instantaneous rate of change of s(t) at t = 1 ... so find s'(t) and evaluate it at t = 1.
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  4. #4
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    Re: rate of change word problem

    Okk for the derivative I got 1500/(t+3)^2 - 3000t/(t+3)^3, and plugged in 1 and got 46.875. Soo it's A.
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