How to solve for k in this model?

I have a question about how to solve for the variable k in this model. Where RK4 is a function that I wrote before.

u0 = 5000; % this is the code that i wrote for problem 2
lambda = 0.03;
pm = 9000;
eqn = lambda*p*(1-p/pm)-k == 500;
Kf = solve(eqn)

u0 = 5000; % this is the code for problem 1
lambda = 0.03;
pm = 9000;
k = 100;
f = @(t,p) lambda*p*(1-p/pm)-k;
[t,P] = RK4(f,u0,100,10)
Pf = P(end)

[Jyotsna Talluri]

What is your function RK4?

Answer 1

[Jyotsna Talluri]

First solve the diffrerential equation and obtain function P as function of t and k using dsolve

syms p(t) pm k  lambda
lambda = 0.03;
pm = 9000;
eqn = diff(p,t) == lambda*p*(1-p/pm)-k
cond = p(0) == 5000;
P(t) = dsolve(eqn,cond);

Solve the equation P(100) = 500 (10% of 5000) for the value of k

k=solve(P(100) == 500,k)