Mathematics, 19.03.2021 20:10 deena7
The park service that administers a state park estimates that there are 495 deer in the park. They decide to remove deer according to the differential equation dP/dt = โ0.1P.
a. Show that the solution to the differential equation dP/dt = โ0.1P is P = 495e^โ0.1t , where t is measured in years and P is the population of deer. Use it to find the deer population in 5 years to the nearest deer.
b. After this 5-year period, no human intervention is taken and the deer population grows again. From that time, the deer population increases directly proportional to 650โP, where the constant of proportionality is k. Find an equation for the deer population P(t) in terms of t and k for this 5-year period.
c. Using the growth model from part b), 1 year later the deer population is 350. Find k.
d. Using the growth model from part b) and the value of k from part c), find lim tโโ P(t)
Answers: 2
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