At time t = 0, a bacterial culture weighs 2 grams. Three 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. (Round your coefficients to four decimal places.) %3D (b) Find the culture's weight after 5 hours. (Round your answer to the nearest whole number.) 9 (c) When will the culture's weight reach 15 grams? (Round your answer to two decimal places.) hr (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. (Round your answer to the nearest whole number.) y(5) = g (e) At what time is the culture's weight increasing most rapidly? (Round your answer to two decimal places.) hr
At time t = 0, a bacterial culture weighs 2 grams. Three 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. (Round your coefficients to four decimal places.) %3D (b) Find the culture's weight after 5 hours. (Round your answer to the nearest whole number.) 9 (c) When will the culture's weight reach 15 grams? (Round your answer to two decimal places.) hr (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. (Round your answer to the nearest whole number.) y(5) = g (e) At what time is the culture's weight increasing most rapidly? (Round your answer to two decimal places.) hr
Chapter5: Exponential And Logarithmic Functions
Section5.5: Exponential And Logarithmic Models
Problem 30E: The table shows the mid-year populations (in millions) of five countries in 2015 and the projected...
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Transcribed Image Text:At time t = 0, a bacterial culture weighs 2 grams. Three 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. (Round your coefficients to four decimal places.)
y =
(b) Find the culture's weight after 5 hours. (Round your answer to the nearest whole number.)
g (c) When will the culture's weight reach 15 grams? (Round your answer to two decimal places.)
hr (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. (Round your answer to the nearest whole number.)
dy
dt
y(5) =
g (e) At what time is the culture's weight increasing most rapidly? (Round your answer to two decimal places.)
hr
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