Hospital patients are often given glucose (blood sugar) through a tube connected to a bottle suspended over their beds. Suppose that this "drip" supplies glucose at the rate of 20 mg per minute, and each minute 25% of the accumulated glucose is consumed by the body. Then the amount y(t) of glucose (in excess of the normal level) in the body after t minutes satisfies the following. Y' = 20 0.25y (Do you see why?) y(0) = 0 (zero excess glucose at t = O) Solve this differential equation and initial condition. W) = 200 200e'0'25' A conservation organization releases 15 Florida panthers into a game preserve. After 3 years, there are 60 panthers in the preserve. The Florida preserve has a carrying capacity of 150 panthers. (a) Write a logistic equation that models the population of panthers in the preserve. (Round your k to four decimal places. Use t for the time in years.) p: (b) Find the population after 5 years. (Round your answer to the nearest whole number.) panthers (c) When will the population reach 75? (Round your answer to two decimal places.) :er (d) Write a logistic differential equation that models the growth rate of the panther population. Then using Euler's Method, repeat part (b) with a step size of h = 1. Use the initial release population of 15 pant'iers as your initial value to start Euler's Method. (Round your answer to the nearest whole number.) i: dt P = E (e) At what time is the panther population growing most rapidly? (Round your answer to two decimal places.) |:lvr