# Exponential growth word problem, pie.

1. Feb 25, 2013

### Matriculator

This whole chapter has been tripping me. My professor made-up another way of doing this, which I'm having a hard time understanding. He's a really intelligent guy(even other professors say it) so he can do this, but I'm having a hard time understanding his way. I went to tutoring today, they couldn't help me with his way. So I'll just try the standard way and see if he'll let it pass.

How would I normally do this? I know that the standard formula is f(t)=Aert?

Would it start like f(2)=150er2? That 70 degrees is my biggest problem. I know that it can't go under 70 degrees, I'm having a hard time knowing how that'll fit into this equation. Thank you in advance.

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2. Feb 25, 2013

### SammyS

Staff Emeritus

The temperature of the pie [STRIKE]cools[/STRIKE] decreases exponentially from whatever temperature it had coming out of the oven to room temperature (70° F). You will need a somewhat different fuction than what you showed.

If f(t) represents the temperature of the pie and t is number of hours after leaving the oven, then:
f(2) = 150°F

f(5) = 130°F​

Last edited: Feb 25, 2013
3. Feb 25, 2013

### eumyang

No, it wouldn't. 150°F is not the initial temperature of the pie. It's the temperature after 2 hours. What you would have is $150 = Ae^{2r}$.

Are you sure you're supposed to use the formula f(t)=Aert? The way I remember learning it, this is Newton's Law of Cooling, and here was the formula:
$T(t) = T_m + (T_0 - T_m)e^{-kt}$,
where
Tm is the temperature of the surrounding medium, and
T0 is the initial temperature of the object.

EDIT: Beaten to it. ;)

Last edited: Feb 25, 2013
4. Feb 25, 2013

### Matriculator

A decaying one? Such as f(t)=Ae-rt? I got this from online. I got that original formula from online. I wasn't too sure of how it worked. Since it allowed me to take the natural log when solving for time on simpler problems, I used it.

5. Feb 25, 2013

### Matriculator

I'm not too sure. Since the chapter is on exponential growth I think that he gave one general formula of some sort to cover all types of exponential growth(interest, bacteria etc..)

6. Feb 25, 2013

### Staff: Mentor

This is not a problem in exponential growth, it is a problem in exponential decay. The thing that is decaying is the difference between the temperature of the pie, and the temperature of the air: (T - 70)
So,

time T T-70
2 150 80
5 130 60

For exponential decay, the constant r in your equation is negative.

7. Feb 25, 2013

### SammyS

Staff Emeritus
I would suggest modifying your temperature function. Try $\displaystyle \ \ f(t) - 70 = Ae^{-rt}\,, \$ where f(t) is the temperature of the pie, and t is time in hours, after the pie has been removed from the oven .

You will need to use logarithms to solve this.

8. Feb 26, 2013

### tia89

Using
the only things you do not know are $k$ and $T_0$. You can then insert the data you have about temperatures and times and you have a system with two equations and two variables (i.e. $k$ and $T_0$). Solve the system and you will have your solution with all parameters.

Finally you just need to insert 7 (hours) and compute the result.

Last edited: Feb 26, 2013