Need help solving this question in MATLAB

Question:

A drug is encapsulated in a polymerand then released slowly into the bloodstream of patients. 100𝜇𝑔 of a drug in a controlled release capsule is injected into a patient. The drug is released at a rate of 8e^(-0.1t^2) 𝜇𝑔/ℎ , where t is hours after injection. Use Matlab toolbox to calculate what fraction of the drug remains in the capsule after 24 h?

I was thinking of using the ode45 solver to solve for the amount of drug remaining in the capsule when t = 24 as shown:

Function File:

function f=Assignment2Q3(D,t)
f=8*exp(-0.1*(t^2));
end

Command Window:

[D,t]=ode45('Assignment2Q3',[0:24],100);

However I have run into 2 problems.

Firstly, the solver does not seem to be working as intended, as I am getting values of D=100 (D is the variable im defining for the amount of drug left in the capsule) for every value from t=0 to t=24.

Next, I do not know how to code the 2nd part of the function that would return me the fraction of the drug in the capsule after 24h after obtaining the value for D when t=24.

A step by step method that details what is being done at each step would be appreciated, as I am very new to MATLAB. Thank you!

Answer 1

[David Hill]

Isn't just an integration of the rate?

f=@(t)8*exp(-.1*t.^2);
FractionRemaing=(100-integral(f,0,24))/100

FractionRemaing = 0.7758

[Gavin Leong]

yep, that pretty much summarizes it. Thanks a lot for your help!