1. Exponential Functions!!

The concentration C in part per million, of a medication in the body t hours after ingestion is give by the function

C(t)= 10t^2e^-t

1. Find the rate of change of the concentration
I know this is the derivative, but the derivative the book give me is not like the one I got. I have

C'(t)=20te^-t - 10t^2e^-t

2. Find the maximum value of the concentration and where it occurs.

2. Originally Posted by littlesohi
The concentration C in part per million, of a medication in the body t hours after ingestion is give by the function

C(t)= 10t^2e^-t

1. Find the rate of change of the concentration
I know this is the derivative, but the derivative the book give me is not like the one I got. I have

C'(t)=20te^-t - 10t^2e^-t

2. Find the maximum value of the concentration and where it occurs.

$C(t)=10t^2e^{-t}$

Apply the product rule:

$C'(t)=20te^{-t}-10t^2e^{-t}$

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$=10e^{-t}(10-t^2)$
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EDIT: I factored that wrong. It should be:

$C'(t)=10te^{-t}(2-t)$

I have no idea how I managed that. It's a good thing pickslides pointed that out.

So you were right about the derivative.

3. Originally Posted by littlesohi

2. Find the maximum value of the concentration and where it occurs.
Solve this

$C'(t)=0$

$te^{-t}(20-10t)=0$

4. Is this correct?

Originally Posted by adkinsjr

$C'(t)=20te^{-t}-10t^2e^{-t}$

$=10e^{-t}(10-t^2)$

$10e^{-t}(10-t^2) = 100e^{-t}-10t^2e^{-t} \neq 20te^{-t}-10t^2e^{-t}$

5. Originally Posted by pickslides
Is this correct? NOPE!

$10e^{-t}(10-t^2) = 100e^{-t}-10t^2e^{-t} \neq 20te^{-t}-10t^2e^{-t}$
I edited the post. It seems I factored that wrong.