Question

The concentration of a drug t hours after being injected is given by C(t) = 0.9t/t^2 + 63. Find the time when the concentration is at a maximum. Give your answer accurate to at least 2 decimal places. hours.

Answer 1

7.94

Explanation:

`\displaystyle C(t)=(0.9t)/(t^2+63)\\\\C'(t)=(0.9(t^2+63)-0.9t(2t))/((t^2+63)^2)\\\\C'(t)=(0.9t^2+56.7-1.8t^2)/((t^2+63)^2)\\\\C'(t)=(-0.9t^2+56.7)/((t^2+63)^2)\\\\0=(-0.9t^2+56.7)/((t^2+63)^2)\\\\0=-0.9t^2+56.7\\\\0.9t^2=56.7\\\\t^2=63\\\\t\approx7.94`

Therefore, the time when the concentration is at a maximum is about 7.94 hours.