The concentration of a drug in the body (in milligrams per milliliter) as a function of time (in hours) since ingestion is given by: $C(t)=14 t e^{-0.10 t}$ How many hours does it take for the drug to reach peak concentration?

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1
4
10
5
100

Answer

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Answer

Final Answer: $\boxed{10}$

Steps

Step 1 ：Define the variable and function: $ t $ is the variable and $ C = 14t e^{-0.10t} $ is the function.

Step 2 ：Compute the derivative of the function: $ C'(t) = -1.4t e^{-0.10t} + 14 e^{-0.10t} $.

Step 3 ：Solve the equation $ C'(t) = 0 $ to find the time at which the drug reaches peak concentration.

Step 4 ：The solution to the equation is $ t = 10 $.

Step 5 ：So, the drug reaches peak concentration 10 hours after ingestion.

Step 6 ：Final Answer: $\boxed{10}$