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.
Unitary Method
The word “unitary” comes from the word “unit”, which means a single and complete entity. In this method, we find the value of a unit product from the given number of products, and then we solve for the other number of products.
Speed, Time, and Distance
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Profit and Loss
The amount earned or lost on the sale of one or more items is referred to as the profit or loss on that item.
Units and Measurements
Measurements and comparisons are the foundation of science and engineering. We, therefore, need rules that tell us how things are measured and compared. For these measurements and comparisons, we perform certain experiments, and we will need the experiments to set up the devices.
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.
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