# Word Problem

## 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

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danago
Gold Member
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?

tiny-tim
Homework Helper
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?

tiny-tim
Homework Helper
70/e^-40b = a
:
10/7 = e^10b

but how do I find a?
a = 70e40b = 70(e10b)4 Thank you !