I need help with part c d and e 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.)5.8025g (c) When will the culture's weight reach 64 grams? (Round your answer to two decimal places.)55.66Xhr (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. (Roundyour answer to the nearest whole number.)-0.0744t(118.56) e1+19e-0.0744t) 2dyy(5) = 5.735.669X hrXg (e) At what time is the culture's weight increasing most rapidly? (Round your answer to two decimal places.)

We have to solve the logistic model equation with given data.

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

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

College Algebra

1st Edition

ISBN:9781938168383

Author:Jay Abramson

Publisher:Jay Abramson

Chapter6: Exponential And Logarithmic Functions

Section: Chapter Questions

Problem 34PT: The population of a lake of fish is modeled by the logistic equation P(t)=16,1201+25e0.75t, where t...

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Question

I need help with part c d and e

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.)
55.66
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.)
-0.0744t
(118.56) e
1+19e-0.0744t) 2
dy
y(5) = 5.73
5.669
X hr
X
g (e) At what time is the culture's weight increasing most rapidly? (Round your answer to two decimal places.)

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