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Gompertz Equation 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 a constant and L is the carrying capacity.
(a) Find the general solution of the differential equation.
(b) Use a graphing utility to graph the slope field for the differential equation when k = 0.05 and L = 1000.
(c) Describe the behavior of the graph in part (b) as
(d) Use a graphing utility to graph the equation you found in part (a) for L = 5000, y(0) = 500, and k = 0.02. Determine the concavity of the graph and how it compares with the general solution of the logistic differential equation.
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Chapter 6 Solutions
Calculus of a Single Variable
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