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

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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
 
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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! :smile:

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 :wink:
 
Thank you !
 
Prove $$\int\limits_0^{\sqrt2/4}\frac{1}{\sqrt{x-x^2}}\arcsin\sqrt{\frac{(x-1)\left(x-1+x\sqrt{9-16x}\right)}{1-2x}} \, \mathrm dx = \frac{\pi^2}{8}.$$ Let $$I = \int\limits_0^{\sqrt 2 / 4}\frac{1}{\sqrt{x-x^2}}\arcsin\sqrt{\frac{(x-1)\left(x-1+x\sqrt{9-16x}\right)}{1-2x}} \, \mathrm dx. \tag{1}$$ The representation integral of ##\arcsin## is $$\arcsin u = \int\limits_{0}^{1} \frac{\mathrm dt}{\sqrt{1-t^2}}, \qquad 0 \leqslant u \leqslant 1.$$ Plugging identity above into ##(1)## with ##u...

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