At time t = 0, a bacterial culture weighs 4 grams. Three hours later, the culture weighs 5 grams. The maximum weight of the culture is 80 grams. (a) Write a logistic equation that models the weight of the bacterial culture. (Round your coefficients to four decimal places.) y = 4e0.0744t ✓ (b) Find the culture's weight after 5 hours. (Round your answer to the nearest whole number.) 5.8025 ✓g (c) When will the culture's weight reach 64 grams? (Round your answer to two decimal places.) 37.27 Xhr (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 -=0.2976e0.0744t X dt y(5) = 5.73 5.80 X hr g (e) At what time is the culture's weight increasing most rapidly? (Round your answer to two decimal places.)
At time t = 0, a bacterial culture weighs 4 grams. Three hours later, the culture weighs 5 grams. The maximum weight of the culture is 80 grams. (a) Write a logistic equation that models the weight of the bacterial culture. (Round your coefficients to four decimal places.) y = 4e0.0744t ✓ (b) Find the culture's weight after 5 hours. (Round your answer to the nearest whole number.) 5.8025 ✓g (c) When will the culture's weight reach 64 grams? (Round your answer to two decimal places.) 37.27 Xhr (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 -=0.2976e0.0744t X dt y(5) = 5.73 5.80 X hr g (e) At what time is the culture's weight increasing most rapidly? (Round your answer to two decimal places.)
College Algebra (MindTap Course List)
12th Edition
ISBN:9781305652231
Author:R. David Gustafson, Jeff Hughes
Publisher:R. David Gustafson, Jeff Hughes
Chapter5: Exponential And Logarithmic Functions
Section5.2: Applications Of Exponential Functions
Problem 34E
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Transcribed Image Text:At time t = 0, a bacterial culture weighs 4 grams. Three hours later, the culture weighs 5 grams. The maximum weight of the culture is 80 grams.
(a) Write a logistic equation that models the weight of the bacterial culture. (Round your coefficients to four decimal places.)
0.0744t
y = 4e
(b) Find the culture's weight after 5 hours. (Round your answer to the nearest whole number.)
5.8025
g (c) When will the culture's weight reach 64 grams? (Round your answer to two decimal places.)
37.27
Xhr (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 = 0.2976e0.0744t X
dt
y(5) = 5.73
5.80
X hr
g (e) At what time is the culture's weight increasing most rapidly? (Round your answer to two decimal places.)
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