1. The population of bacteria is modeled using the following differential equation, P is in terms of bacteria and t is in terms of seconds: dP .25P(8— Р) dt a. Find the following and then on a separate sheet of paper draw a slope field demonstrating the growth of the population. Use the colors indicated for your drawing. 1. Equilibrium solutions (draw in red) II. Isoclines for the following, round to 4 decimal places (show your work): i. K=-15 (negative fifteen, in blue) K=15 (in green) ii. III. Identify where the function is increasing and decreasing. IV. Identify the changes in concavity. Mark these on the y-axes with with the abbreviation CIC.
1. The population of bacteria is modeled using the following differential equation, P is in terms of bacteria and t is in terms of seconds: dP .25P(8— Р) dt a. Find the following and then on a separate sheet of paper draw a slope field demonstrating the growth of the population. Use the colors indicated for your drawing. 1. Equilibrium solutions (draw in red) II. Isoclines for the following, round to 4 decimal places (show your work): i. K=-15 (negative fifteen, in blue) K=15 (in green) ii. III. Identify where the function is increasing and decreasing. IV. Identify the changes in concavity. Mark these on the y-axes with with the abbreviation CIC.
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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Answer A- D and circle the answer.
Transcribed Image Text:1. The population of bacteria is modeled using the following differential equation, P is in terms of
bacteria and t is in terms of seconds:
dP
.25P(8 – P)
dt
a. Find the following and then on a separate sheet of paper draw a slope field
demonstrating the growth of the population. Use the colors indicated for your drawing.
I. Equilibrium solutions (draw in red)
II.
Isoclines for the following, round to 4 decimal places (show your work):
i. K=-15 (negative fifteen, in blue)
ii.
K=15 (in green)
II.
Identify where the function is increasing and decreasing.
IV. Identify the changes in concavity. Mark these on the y-axes with with the
abbreviation CIC.
b. On your slope field, draw solution curves for initial conditions of P=2, P=6, P=11.
c. Find the particular solution for the population when P(0)=12. Show your work.
d. When will the population that you found in C reach 1000 bacteria? Explain your
reasoning.
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