At time t = 0, a bacterial culture weighs 2 grams. Three hours later, the culture weighs 5 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.)20y =dydt=1 +9e8g (c) When will the culture's weight reach 16 grams? (Round your answer to two decimal places.)9.79hr (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 astep size of h = 1. (Round your answer to the nearest whole number.)y(5) =6-0.3662t= 1.370.366y| 1(1-20)(b) Find the culture's weight after 5 hours. (Round your answer to the nearest whole number.)X 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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At time t = 0, a bacterial culture weighs 2 grams. Three hours later, the culture weighs 5 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 = 8 20 1+9e-0.3662t (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 16 grams? (Round your answer to two decimal places.)

At time t = 0, a bacterial culture weighs 2 grams. Three hours later, the culture weighs 5 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 = 8 20 1+9e-0.3662t (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 16 grams? (Round your answer to two decimal places.)

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Question

At time t = 0, a bacterial culture weighs 2 grams. Three hours later, the culture weighs 5 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.)
20
y =
dy
dt
=
1 +9e
8
g (c) When will the culture's weight reach 16 grams? (Round your answer to two decimal places.)
9.79
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) =
6
-0.3662t
= 1.37
0.366y| 1
(1-20)
(b) Find the culture's weight after 5 hours. (Round your answer to the nearest whole number.)
X 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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