Python This simulates the population of fish. Use this to generate a plot with a numerical solution and the exact solution on the same plot axes for model parameters, P_m = 20,000 fish with a birth rate of b=6%, a harvesting rate of h=4%, a change in t=0.5 and y_0=5000
Python
This simulates the population of fish. Use this to generate a plot with a numerical solution and the exact solution on the same plot axes for model parameters, P_m = 20,000 fish with a birth rate of b=6%, a harvesting rate of h=4%, a change in t=0.5 and y_0=5000
![The differential equation has an exact solution
\[
y(t) = \frac{y_0 P_M (h-b)}{(P_M(h-b) + b y_0)e^{(h-b)t} - b y_0}
\]
This equation describes the behavior of a variable \(y\) over time \(t\). It includes parameters such as the initial value \(y_0\), constants \(P_M\), \(h\), and \(b\). It also features an exponential term, which typically indicates a growth or decay process depending on the sign of the exponent.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fa4aac48a-4d20-41e4-aba5-4ec9a336b2fd%2F00183270-d67f-4a9b-b364-a56c7b424b13%2Fwwnivwg_processed.png&w=3840&q=75)
Programmatic access:
Step 1: Import the NumPy and matplotlib modules.
Step 2: Take the initial population from the user and store it in the integer variable y0. Take the birth rate from the user and store it in the b variable. Take the time step size from the user and store it in the float dt variable. Take the number of days from the user and store it in an integer variable n.
Step 3: Create a variable yn for the maximum population and initialize it with a value of 20,000.
Step 4: Create an array t from 0 to (n+1)*dt with n+2 elements.
Step 5: Create an N array with n+2 zeros.
Step 6: Store the initial file y0 as the first element of the N array.
Step 7: Fill in the N fields using the forward Euler method.
Step 8: Plot the graph using xlabels, ylabels, and legends.
Step by step
Solved in 2 steps with 2 images
