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

[betsinda]

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.

Homework Equations

The Attempt at a Solution

I have no idea how to even start. Please help

 

[danago]

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]

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?

 

[betsinda]

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]

70/e^-40b = a
:
10/7 = e^10b
…
but how do I find a?

a = 70e^40b = 70(e^10b)⁴

 

[betsinda]

Thank you !