A population of shrimp in a farm has unlimited resources and its population size grows at a rate of 10% per month. The initial population size is one million. How many shrimp can be harvested each month without ultimately exhausting the population? This problem has an analytical solution, but here, solve it using Euler's method and trial and error to find the harvesting rate.

We can describe this problem with this governing equation which describes the shrimp population as a function of time ()S(t) with

()/=()(1)

where =0.1, (0)=10^6 and H is the (unknown) harvesting rate.

Use Euler's method to calculate an approximate solution to this equation, finding S at time +1ti+1 using the previous value of S at time ti:

(+1)=()+((/)|)

where =+1 is the time step and | is given by the differential equation above. In this problem we use a constant time step when using Euler's method (i.e. =32=21=+1)

Your function should use Euler's method to solve Equation (1) over a long enough time period to be sure the shrimp population is stable. Try different values of . You can use a constant time step of = XXX.

in python.

Plot the shrimp population as a function of time with the maximum harvesting rate you determined (by trial and error, or another method). Label the axes of your plot

We can describe this problem with this governing equation which describes the shrimp population as a function of time S(t) with dS(t) aS(t) H (1) dt where a = 0.1, S(0) = 10 and H is the (unknown) harvesting rate. Use Euler's method to calculate an approximate solution to this equation, finding S at time ti+1 using the previous value of S at time t;: d.s S(ti+1) = S(t;) + ayat where At = ti+1 = t; is the time step and 45 17. is given by the differential equation above. In this problem we use a constant time step when using Euler's method (i.e. At = tz t2 = t2 t1 = tk+1 tk). Your function should use Euler's method to solve Equation (1) over a long enough time period to be sure the shrimp population is stable. Try different values of H. You can use a constant time step of Az = XXX. We can describe this problem with this governing equation which describes the shrimp population as a function of time S(t) with dS(t) aS(t) H (1) dt where a = 0.1, S(0) = 10 and H is the (unknown) harvesting rate. Use Euler's method to calculate an approximate solution to this equation, finding S at time ti+1 using the previous value of S at time t;: d.s S(ti+1) = S(t;) + ayat where At = ti+1 = t; is the time step and 45 17. is given by the differential equation above. In this problem we use a constant time step when using Euler's method (i.e. At = tz t2 = t2 t1 = tk+1 tk). Your function should use Euler's method to solve Equation (1) over a long enough time period to be sure the shrimp population is stable. Try different values of H. You can use a constant time step of Az = XXX