A drug is injected into the body in such a way that the concentration, C, in the blood at time t hours, is given by the function C (t) = 10 (e-2t - e-3t). At what time is the concentration of the drug in the body at the highest? Express your

answer to three decimal places.

0.41 = t

Step-by-step explanation:

Let C represent the amount of concentration

Let t represent time.

Now, differentiate with respect to t

C' (t) = 10 (-2e^-2t + 3e^-3t)

C' (t) = 10 (e^-2t) (-2 + 3e^-t)

0 = e^-2t (This is not valid or cannot be considered)

0 = - 2 + 3e^-t

2/3 = e^-t

ln 2/3 = t

0.41 = t