1 pt) Coroners estimate time of death using the rule of thumb that a body cools about 2 degrees F during the first hour after death and about 1 degree F for each additional hour. Assuming an air temperature of 68 degrees F and a living body temperature of 98.6 degrees F, the temperature T(t) in degrees F of a body at a time t hours since death is given by

Question

T(t)=68+30.6e^(−kt.)
For what value of k will the body cool by 2 degrees F in the first hour?
Using the value of k found above, after how many hours will the temperature of the body be decreasing at a rate of 1 degree F per hour?
Using the value of k found above, show by calculating both values that, 24 hours after death, the coroner's rule of thumb gives approximately the same temperature as the formula.

Answer 1

To answer the 1st question, just plug in t=2 and solve for k:

68+30.6e^(-2k) = 96.6

Now just use the amended formula for the rest. If you get stuck, come on back and show us whatcha got so far.

Answer 2

K=.0337966456

Answer 3

T(t)=68+30.6e^(−kt.)
After one hour the temp has dropped 2 degrees so T(t)=96.6, solve for K
k=0.06759

you just substitute into this equation using your k value for the rest of the equation except for part D which is just 98.6-25=73.6