# Math Help - To find the constant?

1. ## To find the constant?

The concentration of a certain drug in the bloodstream t hours after the drug is administered is given by c(t)=12te^-bt ng/ml where b is some positive constant.Suppose that the drug reached maximum concentration exactly after four hours after being administered.Find the constant b.

2. Originally Posted by mathcalculushelp
The concentration of a certain drug in the bloodstream t hours after the drug is administered is given by c(t)=12te^-bt ng/ml where b is some positive constant.Suppose that the drug reached maximum concentration exactly after four hours after being administered.Find the constant b.
$c(t)=12te^{-bt}$

Differentiate by applying the product rule.

$c'(t)=-b12te^{-bt}+12e^{-bt}$

You're given that this function is maximum at $t=4$

$c'(4)-48be^{-4b}+12e^{-4b}=0$

$48b=12$

$b=\frac{1}{4}$