In your previous work for DCNR, you predicted that if there are 1000 nittany mice now, then in five years there will be approximately 7389 mice, assuming the mice population obeys the differential equation P' = 0.4P. Now suppose DCNR has called you back, very alarmed, as they have extracted DNA samples from the nittany mice and found that it's like nothing else on Earth, so they suspect the mice have been introduced by some hostile alien species from another planet. Field counts have revealed that the mouse population is growing much more rapidly than they thought. After analyzing the data, you determine that the population satisfies the differential equation P' = 0.4Ppl.1 (a) Assuming there are 1000 mice now, how many will there be in five years? Compare your result to the prediction from the previous model P' = 0.4P. (b) Will there be a doomsday? If so, when will it come?

In your previous work for DCNR, you predicted that if there are 1000 nittany mice now, then in five years there will be approximately 7389 mice, assuming the mice population obeys the differential equation P' = 0.4P. Now suppose DCNR has called you back, very alarmed, as they have extracted DNA samples from the nittany mice and found that it's like nothing else on Earth, so they suspect the mice have been introduced by some hostile alien species from another planet. Field counts have revealed that the mouse population is growing much more rapidly than they thought. After analyzing the data, you determine that the population satisfies the differential equation P' = 0.4Ppl.1 (a) Assuming there are 1000 mice now, how many will there be in five years? Compare your result to the prediction from the previous model P' = 0.4P. (b) Will there be a doomsday? If so, when will it come?

Calculus: Early Transcendentals

8th Edition

ISBN:9781285741550

Author:James Stewart

Publisher:James Stewart

Chapter1: Functions And Models

Section: Chapter Questions

Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...

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Concept explainers

Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.

Question

100%

In class we have considered population models of the form P' = aP", where r > 1. In the case r = 1,
we get the exponential growth model P' = aP. Positive solutions grow exponentially but do not lead
to a "doomsday" scenario. But if r = 2, we get the differential equation P' = aP², and in that case,
positive solutions do produce a “doomsday" scenario.
So what about some exponent r satisfying 1 < r < 2? Suppose we try r = 1.1 in the following silly
case:
In your previous work for DCNR, you predicted that if there are 1000 nittany mice now, then in
five years there will be approximately 7389 mice, assuming the mice population obeys the differential
equation P' = 0.4P. Now suppose DCNR has called you back, very alarmed, as they have extracted
DNA samples from the nittany mice and found that it's like nothing else on Earth, so they suspect
the mice have been introduced by some hostile alien species from another planet. Field counts have
revealed that the mouse population is growing much more rapidly than they thought. After analyzing
the data, you determine that the population satisfies the differential equation P' = 0.4P1.1
%3D
(a) Assuming there are 1000 mice now, how many will there be in five years? Compare your result
to the prediction from the previous model P' = 0.4P.
(b) Will there be a doomsday? If so, when will it come?

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On the early detection period of COVID-19, there were 557 people verified to have been infected by the virus. This rate of increase is modeled using the differential equation below, with N being the number of people, and t for the time elapsed (in days) since it was detected on January 22, 2020. dN = (37602 – 1002.42t + 14.6982t² – 0.0204t")dt With the creation of the vaccines, the modeled equation shifted to the one below. The variable N, is the number of people still infected due to mishandling of the vaccine, resulting to unavailability for some countries. dN = (42023 – 1155.8t + 15.8388t² – 0.0228t³)dt Determine the number of people that can be saved by the vaccine if it is to be administered on March 8, 2021, on the assumption that no sideeffects and complications will be triggered.
INTRODUCTION TO DIFFERENTIAL EQUATIONS HOMEWORK 0-weeks 1,2,3,4 DEPARTMEN T OF MATHEMATICS Lecturer: Doç. Dr. Tahsin ÖN ER Name and Sur name: Student ID: Signature: 1. Find the value(s) of m so that the function y em is a solution of 2y"+7y-4y 0.
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