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Word Problem

  • Thread starter betsinda
  • Start date
  • #1
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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
 

Answers and Replies

  • #2
danago
Gold Member
1,122
4
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?
 
  • #3
tiny-tim
Science Advisor
Homework Helper
25,832
249
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! :smile:

Hint: what is Newton's law of cooling?
 
  • #4
12
0
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?
 
  • #5
tiny-tim
Science Advisor
Homework Helper
25,832
249
70/e^-40b = a
:
10/7 = e^10b

but how do I find a?
a = 70e40b = 70(e10b)4 :wink:
 
  • #6
12
0
Thank you !
 

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