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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Transcribed Image Text: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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