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Math Help - Word problem: Dealing with functions

  1. #1
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    Word problem: Dealing with functions

    The circulation of a magazine is currently 100,000, and decreasing. They have hired a consulting firm who have come up with a brilliant plan to turn the magazine's fortunes around, and claim that the circulation (in thousands) after t years will be

    C(t) = 100 - 30t - 5t^2 - 0.2t^3
    ]
    [ The model is only valid for t >(or equal) 0, and C(t) >(or equal) 0. ]

    a) What is the circulation after 8 years?
    b) Use the derivative to estimate the circulation after 9 years.
    c) When does the circulation reach 100,000 again?
    d) What is the maximum circulation?

    Please tell me if I'm on the right track:

    a) I put 8 for t and solve.

    b) The derivative is - 30 + 10t - .6t^2. Now in this I put 9 for t and solve

    c) Have no idea. 100, 000 = C(t)

    d) No clue.

    Thanks.
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  2. #2
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    Re: Word problem: Dealing with functions

    Quote Originally Posted by hollylovespunk View Post

    a) I put 8 for t and solve.
    Yep.

    Quote Originally Posted by hollylovespunk View Post

    b) The derivative is - 30 + 10t - .6t^2. Now in this I put 9 for t and solve
    This will give you the rate of change in the 9th year.




    Quote Originally Posted by hollylovespunk View Post


    c) Have no idea. 100, 000 = C(t)

    Yep, solve for t


    Quote Originally Posted by hollylovespunk View Post

    d) No clue.
    Solve for the C'(t) = 0
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  3. #3
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    Re: Word problem: Dealing with functions

    Thank you pickslides. Everything makes sense except d. How does solving for C'(t) = 0 tell us the maximum circultation? If you could just explain the logic I will solve these so you guys can check my work.
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  4. #4
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    Re: Word problem: Dealing with functions

    C'(t) gvies the gradient, when the gradient is zero implies a maximum or minimum.
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