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Math Help - Function

  1. #1
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    Function

    The temperature of a cup of coffee t minutes after it has been poured is described by the function C(t) = 20 + 60(0.95)^t .

    a. How many minutes does it take for the coffee to cool to a temperature of d degrees?


    b. About how fast is the temperature dropping when t = 1?

    For a. is it just:  d = 20 + 60(0.95)^t ??

    Could someone help me with both a and b pls?
    Thanks.

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  2. #2
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    Quote Originally Posted by foreverbrokenpromises View Post
    The temperature of a cup of coffee t minutes after it has been poured is described by the function C(t) = 20 + 60(0.95)^t .

    a. How many minutes does it take for the coffee to cool to a temperature of d degrees?


    b. About how fast is the temperature dropping when t = 1?

    For a. is it just:  d = 20 + 60(0.95)^t ??

    Could someone help me with both a and b pls?
    [FONT=Arial]Thanks.
    For a, yes but I would write C(t) = 20 + 60(0.95)^t=d

    For b, C(t) = 20 + 60(0.95)^t\rightarrow C'(t)=60ln\left(\frac{19}{20}\right)\left(\frac{19  }{20}\right)^t

    C'(1)=60ln\left(\frac{19}{20}\right)\left(\frac{19  }{20}\right)^1=57\left(\frac{19}{20}\right)= 54.15
    Last edited by dwsmith; May 18th 2010 at 08:02 PM. Reason: Misread question
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