A state game commission releases 40 wolves into an enclosed game refuge. After 7 years the wolf population is 173. The commission believes the game refuge can support a maximum of 3000 wolves (This is known as the carrying capacity). Assume the number of wolves is measured by y and time is measured by t.Assume the rate of growth of the population is proportional to the product of y and (1-(y/L)),where L is the carrying capacity. a) Determine the differential equation for the wolf population in terms of y=y(t). b) Determine the particular solution of the differential equation modelling the wolf population. The integration constant and constant of proportionality must be solved for exact solutions. c) Estimate the number of years it will take the game refuge to establish 1250 wolves in the game refuge.You will be graded on the exact solution.
A state game commission releases 40 wolves into an enclosed game refuge. After 7 years the wolf population is 173. The commission believes the game refuge can support a maximum of 3000 wolves (This is known as the carrying capacity). Assume the number of wolves is measured by y and time is measured by t.Assume the rate of growth of the population is proportional to the product of y and (1-(y/L)),where L is the carrying capacity.
a) Determine the differential equation for the wolf population in terms of y=y(t).
b) Determine the particular solution of the differential equation modelling the wolf population. The
c) Estimate the number of years it will take the game refuge to establish 1250 wolves in the game refuge.You will be graded on the exact solution.
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