Math
posted by Hannah on .
An object is heated to 90 degrees Celcius and is then allowed to cool in a room whose air temperature is 25 degrees celcius. If the temperature of the object is 75 degrees celcius after 10 minutes, when will its temperature be 50 degrees celcius?

You will need Newton's Law of Cooling formula, which is
T(t) = T_{m} + (T_{0}  T_{m})e^(kt)
where T(t) is the current temperature of the object
T_{m} is the surrounding temperature and
T_{0}is the starting temperature
t is in minutes, and k is a constant
first we have to find the value of k
75 = 25 + (9025)e^(10k)
50 = 65 e^(10k)
.76923 = e^(10k)
10k = ln .76923
k = .026236
so now
50 = 25 + (9025)e^(.026236t)
25/65 = e^(.026236t)
(.026236t) = ln(25/65)
t = 36.42 minutes 
Thank you!!!