QUESTION 13 In a magical land, Alice discovers a warren of rabbits that reproduce rapidly. Initially, there were 100 rabbits in the warren. Their population doubles every 6 months. Alice realizes that if the population growth continues unchecked, the warren will run out of food when the population reaches 5000 . a. Write the differential equation t

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QUESTION 13 In a magical land, Alice discovers a warren of rabbits that reproduce rapidly. Initially, there were 100 rabbits in the warren. Their population doubles every 6 months. Alice realizes that if the population growth continues unchecked, the warren will run out of food when the population reaches 5000 . a. Write the differential equation that describes the rabbit population

P(t)

at any time

t

, where

t

is measured in months. b. Solve the differential equation to find the population

P(t)

as a function of time. c. What will the population size be in 10 months? d. How many months will it take for the population to reach 5000 rabbits? (9 marks)

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