Pre-calculus word problem..... help please?

Question

The temperature of an object, initially at 70 degree, heats up to a surrounding temperature of 350 degree. Find an exponential function for the temperature of the object if the temperature is 110 degree two minutes after it begins to heat. Also, find the average rate of change in the temperature from t = 10 minutes to t = 20 minutes.

Answer 1

Since the rate of heating should diminish as the temperature approaches that of the 350 degree surroundings, an exponential of the form

(350-T)= 280 exp (- b t)   should work.

Here T is the temp at any time

exp (  ) is the same as "e" raised to a power

b is a constant to be determined

t is the time

Since we know that at t=2, T=110, b can be computed.

Once that is done, we can compute the T at 10 and 20 minutes, and the difference between these divided by 10 minutes is the average rate of change.  

Answer 2

"Pre-calculus"?  This is a diff-eq problem!

Newton's law of cooling --

dT/dt = -kT

with solution

T = T(subzero) * exp(-k * t)

Just plug in your initial conditions.