(adsbygoogle = window.adsbygoogle || []).push({}); Modeling with exponential and logarithmic functions help???

1. The problem statement, all variables and given/known data

Use Newton's Lay of Cooling,T = C + (T, to solve this exercise. At 9:00 A.M., a coroner arrived at the home of a person who had died during the night. The temperature of the room was 70 degrees F, and at the time of death the person had a body temperature of 98.6 degrees F. The coroner took the body's temperature at 9:30 A.M., at which time it was 85.6 degrees F, and again at 10:00 A.M., when it was 82.7 degrees F. At what time did the person die?_{0}- C)e^{-kt}

2. Relevant equations

T = C + (T_{0}- C)e^{-kt}

If you do not know what the variable's mean...these are their meanings:

T = temperature of a heated object

C = constant temperature of the surrounding medium (the ambient temp)

T_{0}= initial temperature of the heated object

k = negative constant associated with the cooling object

t = time (in minutes)

3. The attempt at a solution

I tried solving for k by doing:

Steps (I plugged all the values in to their corresponding places):

85.6 = 70 + (98.6 - 70)e^{-k(30)}

15.6 = 28.6e^{-30k}

0.5454545455 = e^{-30k}

ln(0.5454545455) = ln(e^{-30k})

ln(0.5454545455) = -30k

k = (ln(0.5454545455)/(-30))

k = 0.0202045268

After getting this....i do not know what to do next...of even if I did the process of anything correctly as yet.

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# Homework Help: Modeling with exponential and logarithmic functions help?

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