Suppose the initial population is Po = 170, the point of inflection is (16,1200), and the time is measured in months. Answer the following parts (a) through (c) using the inhibited growth model dP = kP(L - P). dt a) Find the limiting population L. b) Use the result of part (a) to find k; then find the particular solution P. c) When will the population reach 800? a) L= (Type an integer or a decimal.) b) k = Type an integer or decimal rounded to seven decimal places as needed.) P(t) =D (Type an exact answer in terms of e. Use integers or decimals for any numbers in the expression. Round to three decimal places as needed.) c) The population will reach 800 in (Type an integer or decimal rounded to three decimal places as needed.) months.

Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter2: Systems Of Linear Equations
Section2.5: Iterative Methods For Solving Linear Systems
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Suppose the initial population is Po = 170, the point of inflection is (16,1200), and the time is measured in months. Answer the following parts (a) through (c) using the inhibited growth model
dP
= kP(L - P).
dt
a) Find the limiting population L.
b) Use the result of part (a) to find k; then find the particular solution P.
c) When will the population reach 800?
a) L=
(Type an integer or a decimal.)
b) k =
(Type an integer or decimal rounded to seven decimal places as needed.)
nt- P(t) =
(Type an exact answer in terms of e. Use integers or decimals for any numbers in the expression. Round to three decimal places as needed.)
c) The population will reach 800 in months.
(Type an integer or decimal rounded to three decimal places as needed.)
kup
NSD
DELL
Transcribed Image Text:Suppose the initial population is Po = 170, the point of inflection is (16,1200), and the time is measured in months. Answer the following parts (a) through (c) using the inhibited growth model dP = kP(L - P). dt a) Find the limiting population L. b) Use the result of part (a) to find k; then find the particular solution P. c) When will the population reach 800? a) L= (Type an integer or a decimal.) b) k = (Type an integer or decimal rounded to seven decimal places as needed.) nt- P(t) = (Type an exact answer in terms of e. Use integers or decimals for any numbers in the expression. Round to three decimal places as needed.) c) The population will reach 800 in months. (Type an integer or decimal rounded to three decimal places as needed.) kup NSD DELL
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