Help with 1 please! I don't know how to approach these questions and the textbook is really confusing me! Problem Set 6.5In Problems 1-4, solve the given differential equation subject tothe given condition. Note that y(a) denotes the value of y at t = a.-6y. y(0) = 41.3.4.5 31 313dydidydtdydt0.005 y, y(10) = 2-0.003 y. y(-2) = 32.dydt=6y, y(0) = 15. A bacterial population grows at a rate proportional to itssize. Initially, it is 10,000, and after 10 days it is 20,000. What is thepopulation after 25 days? See Example 2.6. How long will it take the population of Problem 5 to dou-ble? See Example 1.7. How long will it take the population of Problem 5 totriple? See Example 1.8. The population of the United States was 3.9 million in1790 and 178 million in 1960. If the rate of growth is assumed pro-portional to the number present, what estimate would you givefor the population in 2000? (Compare your answer with the ac-tual 2000 population, which was 275 million.)at 3.2%whorreraftboofdofre51inwilbromiperminplathe

Given: dydt=-6y, y0 = 4 To solve the above given differential equation , we will use variable…

Answered: dy dt - -6y, y(0) = 4

Math

Calculus

dy dt - -6y, y(0) = 4

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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Question

Help with 1 please!
I don't know how to approach these questions and the textbook is really confusing me!

Problem Set 6.5
In Problems 1-4, solve the given differential equation subject to
the given condition. Note that y(a) denotes the value of y at t = a.
-6y. y(0) = 4
1.
3.
4.
5 31 313
dy
di
dy
dt
dy
dt
0.005 y, y(10) = 2
-0.003 y. y(-2) = 3
2.
dy
dt
=
6y, y(0) = 1
5. A bacterial population grows at a rate proportional to its
size. Initially, it is 10,000, and after 10 days it is 20,000. What is the
population after 25 days? See Example 2.
6. How long will it take the population of Problem 5 to dou-
ble? See Example 1.
7. How long will it take the population of Problem 5 to
triple? See Example 1.
8. The population of the United States was 3.9 million in
1790 and 178 million in 1960. If the rate of growth is assumed pro-
portional to the number present, what estimate would you give
for the population in 2000? (Compare your answer with the ac-
tual 2000 population, which was 275 million.)
at 3.2%
wh
or
rer
aft
bo
of
do
fre
51
in
wil
bro
mi
per
min
pla
the

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