# maximun quantity

• Oct 27th 2008, 05:09 PM
ab32
maximun quantity
The quantity of a medication in the bloodstream t hours after it is ingested is given, in mg, by q(t) = 200te(-t). How much of the medication is in the bloodstream at time t = 0? What is the maximum quantity of the medication in the bloodstream and what is the corresponding time t?
• Oct 27th 2008, 07:00 PM
mr fantastic
Quote:

Originally Posted by ab32
The quantity of a medication in the bloodstream t hours after it is ingested is given, in mg, by q(t) = 200te(-t). How much of the medication is in the bloodstream at time t = 0? What is the maximum quantity of the medication in the bloodstream and what is the corresponding time t?

Substitute t = 0.

Solve dq/dt = 0 for t. Substitute this value of t into q(t).
• Oct 28th 2008, 12:04 PM
ab32
the deriv is -400te right??? when u plug 0 in i get zero ???? i think thats wrong??
• Oct 29th 2008, 01:49 PM
mr fantastic
Quote:

Originally Posted by ab32
the deriv is -400te right??? when u plug 0 in i get zero ???? i think thats wrong??

Use the product rule to get the derivative of \$\displaystyle 200 t e^{-t}\$. Note that the derivative of \$\displaystyle e^{-t}\$ is \$\displaystyle -e^{-t}\$.