Answer to Question 4

Jello: T(t) = 36 + (85 - 36)e-kt
where t = time taken for the cooling
T(t) = temperature of the jello at time t
k = decay constant

a) Temperature after 20 minutes = 60º F.
T(20) = 60 = 36 + (85 - 36)e-k•20
60 = 36 + 49e-20k
24 = 49e-20k
24/49 = e-20k
ln(24/49) = ln e-20k
-0.7137664678 = -20k
0.0356883234 = k

b) T(t) = 40 = 36 + 49e-0.0356883234t
4 = 49e-0.0356883234t
4/49 = e-0.0356883234t
ln(4/49) = ln e-0.0356883234t
-2.505525937 =-0.0356883234t
70.20576195 ≈ t ≈ 70 minutes

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