Newton's Law of Cooling Euler's method, don't understand how it works in matlab

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Hello!
My professor has only given one example on Euler's method, so I'm really working from scratch here and would like guidance on starting Euler's method for this problem:
I apologize for asking a question with none of my own coding given. A starter or pseudocode for the Euler's would be immensely helpful!
You are working as a crime scene investigator and must predict the temperature of a homicide victim over a 5 hour period . You know that the room where the victim was found was at 10 ∘ C when the body was discovered.
Use Newton's law of cooling and Euler's method to compute the victim's body temperature for the 5 hour period using values of k = 0.12/hr and Δ t = 0.5 h r. Assume that the victim's body temperature at the time of death was 37 ∘ C , and that the room temperature was at a constant value of 10 ∘ C over the 5 hour period.
dT/dt = -k(T-T_a)
Newton's law of cooling says that the temperature of a body changes at a rate proportional to the difference between its temperature and that of the surrounding medium (the ambient temperature)
This is what I have so far:
for i=1:12
T(i+1,2)= T(i,2)+0.5*k*(T(i+1,1)-T_f);
end

Accepted Answer

KALYAN ACHARJYA
KALYAN ACHARJYA on 17 Jan 2021
As you have tried, so sufficient Hint here
dt=0.5;
T_amb=10;
t=0:dt:5; % Check
T=zeros(1,length(t));
T(1)=37;
k=0.12;
for i=1:length(t)-1
dTdt=-k*(T(i)-T_amb);
T(i+1)= T(i)+0.5*dTdt;
end
plot(t,T);
grid on;

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