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 62 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 $$T(t) = 62 + 36.6 e^{-kt}.$$

1. For what value of $k$ will the body cool by 2 degrees F in the first hour?
$k=$

2. 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?
after hours

3. 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.
$T(24)=$ degrees F
rule of thumb gives T = degrees F