d) Prove that the rate of growth, dt is given by NP (500 N) %3D dt 4000

Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter7: Distance And Approximation
Section7.3: Least Squares Approximation
Problem 35EQ
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2. A biologist is investigating the growth of a population of a species of rodent. The biologist
proposes the model
500
1+ 9e-
For the number of rodents, N, in the population t weeks after the start of the investigation.
Use this model to answer the following questions.
a) Calculate the size of the population at the start of the investigation.
b) Calculate the size of the population 24 weeks after the start of the investigation.
Give the answer to the nearest whole number.
c) Determine the number of weeks that it will take the population to reach 400. Give
the answer in the form t = r In s, wherer and s are integers.
d) Prove that the rate of growth,
dN
,is given by
dt'
dN
(500 N)
4000
dt
Transcribed Image Text:2. A biologist is investigating the growth of a population of a species of rodent. The biologist proposes the model 500 1+ 9e- For the number of rodents, N, in the population t weeks after the start of the investigation. Use this model to answer the following questions. a) Calculate the size of the population at the start of the investigation. b) Calculate the size of the population 24 weeks after the start of the investigation. Give the answer to the nearest whole number. c) Determine the number of weeks that it will take the population to reach 400. Give the answer in the form t = r In s, wherer and s are integers. d) Prove that the rate of growth, dN ,is given by dt' dN (500 N) 4000 dt
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