# Solve Word Problem: Find a and b in T(t)=250-ae^(-bt)

• betsinda
In summary, the conversation discusses finding the values of a and b in the equation T(t)=250-ae^(-bt), which models the temperature of a yam in an oven. By using the given information of the temperature at 30 minutes and the rate of increase, b can be found using Newton's law of cooling. To find a, the equation 70/e^-40b = a is used with the value of b calculated previously.

## Homework Statement

A yam is pust in an oven maintained at a constant temp of 250degrees C. Suppose that after 30 min the temp of the yam is 150degrees C and is increasing at a rate of 3degrees C/min. If the temp of the yam t minutes after it is put in the oven is modeled by
T(t)=250-ae^(-bt), find a and b.

## The Attempt at a Solution

Just by looking at the question as stated, what are the values of:

T(30)
T'(30) ?

How can you use these to find a and b?

betsinda said:
A yam is pust in an oven maintained at a constant temp of 250degrees C. Suppose that after 30 min the temp of the yam is 150degrees C and is increasing at a rate of 3degrees C/min. If the temp of the yam t minutes after it is put in the oven is modeled by
T(t)=250-ae^(-bt), find a and b.

Hi betsinda! Hint: what is Newton's law of cooling?

I think I have found b

180 = 250 - ae^-40b
150 = 250 - ae^-30b

-70 = -ae^-40b
70/e^-40b = a

-100 = -70/e^-40b * e^-30b
100/70 = e^40b * e ^-30b
10/7 = e^10b
ln 10/7 = 10 b
b = ln(10/7)/10

but how do I find a?

betsinda said:
70/e^-40b = a
:
10/7 = e^10b

but how do I find a?

a = 70e40b = 70(e10b)4 Thank you !