Question: Another model that can be used to represent population growth is the Gompertz equation, which is the solution of the differential equation where k is

Another model that can be used to represent population growth is the Gompertz equation, which is the solution of the differential equation

dy dt (7) x y y = k ln

where k is a constant and L is the carrying capacity.

(a) Solve the differential equation.

(b) Use a graphing utility to graph the slope field for the differential equation when k = 0.05 and L = 1000.

(d) Graph the equation you found in part (a) for L = 5000,
Y₀ = 500, and k = 0.02. Determine the concavity of the graph and how it compares with the general solution of the logistic differential equation.

dy dt (7) x y y = k ln

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