Suppose P(t) represents the population of a certain mosquito colony, where t is measured in days. Thecurrent population of the colony is known to be 563 mosquitos; that is, P(0) = 563. If P'(0) = 161mosquitos per day, estimate the size of the population in 11 days.%3DMosquitos (round to nearest whole number)Question Help: Message instructorSubmit QuestionJump to Answer

Answered: Suppose P(t) represents the population…

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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Suppose P(t) represents the population of a certain mosquito colony, where t is measured in days. The
current population of the colony is known to be 563 mosquitos; that is, P(0) = 563. If P'(0) = 161
mosquitos per day, estimate the size of the population in 11 days.
%3D
Mosquitos (round to nearest whole number)
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The population is increasing per day by a fixed number. So the population follows a linear model of the form $y = m x + b$ , where m is the slope of the line and $(0, b)$ is the y-intercept. Thus the population follows the model $P (t) = P (0) + P' (0) t$ , where P(t) is the population at time t, P(0) is the initial population and P'(0) is the increase in population per day.

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