maximum quantity - check work please

[njoyce]

The quantity of a medication in the bloodstream t hours after it is ingested is given, in mg, by q(t) = 200te^-t. What is the maximum quantity of the medication in the bloodstream?

A) 74 mg
B) 200 mg
C) 544 mg
D) 100 mg

I got C) 544 mg.

q'(t) = 200e^-t + 200te^-t
= 200e^-t (1 + t)
1 + t = 0
t = -1

Then I plugged t = -1 back into the original function and got 543.66 which rounds up to 544.

I would appreciate it if someone could check my work

Thanks

 

[tkhunny]

1) Your answer should make at least a little sense. How could the answer be at t = -1? The maximum level is one hour BEFORE taking the medication?! I think not.

2) Try that derivative again. You just missed one sign. If f(x) = e^(-x), then f'(x) = -e^(-x). You missed the negative out in front.

 

[pka]

A) 74 mg
q'(t) = 200e^-t-200te^-t
= 200e^-t (1 - t)

You see that you made a sign error.
t=1 so A is the answer.

 

[njoyce]

I see it. Thank you.

 

[tkhunny]

3) Excellent job showing us your work. It made it very simple to track down the error. Thank YOU!