# Question: you have just boiled a new batch of broth for...

###### Question details

You have just boiled a new batch of broth for your important culture of E. coli, so it is at 100C. You have it sitting in a room that is at 24 C, and you find 8 minutes later that it's cooled to 94 C. You want to innoculate the culture when it reaches 38 C. You are interested in knowing if you can safely go off to exercise while the broth cools.

a. Let T(t) be the temperature of the broth. Assume that the broth satisfies Newton's Law of Cooling. Find the cooling constant K=

b. Give the solution to this problem (using the value of K that you found) T(t)= (Celcius)

c. Find how long it will be until you need to innoculate the
broth with your culture.

(min)