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lola
lola asked in Science & MathematicsMathematics · 6 years ago

If you pour a cup of coffee that is 200 F, and set it on desk in a room that is 68 F, and 10 minutes later it is 145 F,...?

If you pour a cup of coffee that is 200 F, and set it on desk in a room that is 68 F, and 10 minutes later it is 145 F, what temperature will it be 15 minutes after you originally poured it?

If t=0, P = 200

\[P_{t} = 132e^{-kt}+68\]

\[145 = 132e^{-10k}+68\]

\[\rightarrow k = 0.0539\]

\[P_{15} = 132e^{-.0539*15}+68\]

\[P_{15} = 126.81\]

so its 127??

Did I do it correctly? If not, please help me!

2 Answers

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  • az_lender
    Lv 7
    6 years ago
    Favorite Answer

    dP/dt = -k(P-68)

    ln(P-68) = -kt + C

    P = 68 + ce^(-kt)

    200 = 68 + ce^(-0) => c = 132, I agree.

    145 = 68 + 132e^(-k*10)

    77/132 = e^(-k*10) =>

    ln(132/77) = 10*k =>

    k = 0.0539, I agree.

    Yeah, probably P15) = 127...

  • Aidan
    6 years ago

    wat. How do i math

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