I have been working on this question for a while and i am stuck.

this is the question.

A patient is given a drug treatment by injections.

If a patient is injected a drug at time t = 0, then the concentration of the drug in the

patient’s blood at later times t is given by

C(t) = At^2e^−t/3

Where A is a constant.

1. What is the total amount of drug administered at time t = 0?

2. Suppose a patient is given 1 unit of the drug at time t = 0. Plot the concentration of

the drug at later times, for t 2 [0, 30]. Determine the maximum concentration of the

drug and the time at which it occurs.

3. A patient is injected with 1 unit of the drug at two times each: the first injection occurs

at time t = 0, and the second injection takes place at time t = 12. (A total of 2 units

is injected).

1. Plot the concentration of the drug at times t 2 [0..50].

2. What is the maximum concentration of the drug, and when does it occur?

4. A patient receives four injections of the drug at times t = 12n for n = 0, 1, 4, 6.

1. Plot the concentration of the drug at times t 2 [0..200].

2. What is the maximum concentration of the drug, and when does it occur?

I neglected A since it is a constant and plotted the function just without A and was able to find that the maximum was at t=6.

now,when they say that he is being injected twice,at t=0 and at t=12 i am not sure what to do.

is it that the function is added again when t=12 and if so how do i write such a thing in maple?how do i write it on paper as a matter a fact!

some help will be well appreciated.