Please help :)

Question

A potato is put into an oven that has been heated to 350F. Its temperature as a function of time is given by T(t) = a(1 - e-kt) + b. The potato was 50F when it was first put into the oven.

What is the value of b in this context? Explain.

What is the value of a in this context? Explain.

Thanks :D

Answer 1

e^-kt -> 0 as x->∞
1-e^-kt -> 1

So, T(t) -> a+b

at t=0, T(t) = b

So, b is the initial temperature of the potato, 50°F

a is the initial temperature difference between the potato and the oven: 300 in this case. You know this because it is clear that as time passes, the temperature of the spud approaches the temp of the oven.