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Math Help - Coffee Cup Problem

  1. #1
    Newbie mockingjay95's Avatar
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    Coffee Cup Problem

    1a. You pour a cup of coffee. When it is poured it is at D=130F above room temp. 3 mins later it has cooled to D=117F above room temp. As the coffee cools the instantaneous rate of change of D with respect to time t min is directly proportional to D. Find the constants in the equation.
    b. The coffee in a. is drinkable if it is at least 50F above room temp. Will it still be drinkable if you let it sit for 15 min after you pour it?

    So for a. I wrote an equation dD/dt=kD , where k is the constant
    then when I integrate it I get ln (abs) D= kt+C <=> D=e^kt+C <=>D=Ce^kt
    Since D=130 when t=0, I solved for C, which is 130.
    Since D=117 when t=3, I solved for k, which is -0.0351
    My equation is now D=130e^-0.0351t
    Please help me with part b?
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  2. #2
    Newbie mockingjay95's Avatar
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    Re: Coffee Cup Problem

    This is my solution for part b, when t=15 minutes, D=130e^-0.035*15=70.99F above room temp, which is drinkable. Is it correct?
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