At time t = 0, a bacterial culture weighs 1 gram. Two hours later, the culture weighs 4 grams. The maximum weight of the culture is 20 grams. (a) Write a logistic equation that models the weight of the bacterial culture. (b) Find the culture’s weight after 5 hours. (c) When will the culture’s weight reach 18 grams? (d) Write a logistic differential equation that models the growth rate of the culture’s weight. Then repeat part (b) using Euler’s Method with a step size of h = 1. Compare the approximation with the exact answer. (e) At what time is the culture’s weight increasing most rapidly? Explain.

At time t = 0, a bacterial culture weighs 1 gram. Two hours later, the culture weighs 4 grams. The maximum weight of the culture is 20 grams. (a) Write a logistic equation that models the weight of the bacterial culture. (b) Find the culture’s weight after 5 hours. (c) When will the culture’s weight reach 18 grams? (d) Write a logistic differential equation that models the growth rate of the culture’s weight. Then repeat part (b) using Euler’s Method with a step size of h = 1. Compare the approximation with the exact answer. (e) At what time is the culture’s weight increasing most rapidly? Explain.