Question 1053355
Newton's law of cooling can be written as T(t) = Ta + (T0-Ta)*exp(-kt), 
where Ta = ambient temperature, T0 = initial temperature and k is a constant
In this problem, T0 = 79 degrees (the initial temperature) Ta = 37 degrees (constant temperature)
So the general formula for temperature vs. time is: T(t) = 37 + (79-37)exp(-kt) = 37 + 42*exp(-kt)
The temperature after 13 mins is 74 deg:
T(13) = 37 + 42*exp(-13k)
Solve for k: k = -ln(37/42)/13 = 0.00975
So the temperature equation is T = 37 + 42*exp(-0.00975t)
54 = 37 + 42*exp(-0.00975t)
Solve for t:
ln(17/42)/-0.00975 = t = 93 mins.
The temperature graph looks like:
{{{ graph( 300, 200, -10, 100, -10, 90, 37+42*exp(-0.00975*x)) }}}