anonymous
  • anonymous
The population of a town grows at a rate proportional to the population present at time t. The initial population of 5000 people is increased by 15% in the period of 10 years. What will the estimated population be in 30 years time?
Differential Equations
  • Stacey Warren - Expert brainly.com
Hey! We 've verified this expert answer for you, click below to unlock the details :)
SOLVED
At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.
chestercat
  • chestercat
I got my questions answered at brainly.com in under 10 minutes. Go to brainly.com now for free help!
anonymous
  • anonymous
have any ideas wat to do? :)
anonymous
  • anonymous
or how to start off?
anonymous
  • anonymous
do you know an equation that works for this kind of thing?

Looking for something else?

Not the answer you are looking for? Search for more explanations.

More answers

anonymous
  • anonymous
no need for one
anonymous
  • anonymous
but it's helpful
anonymous
  • anonymous
yes. i work it out until i got P = Ae^(0.15t)
anonymous
  • anonymous
since 10yrs=15% then 30yrs=45% thus the population growth in 30 yrs is 5000 x 145/100 50 x 145
anonymous
  • anonymous
the equation you can find for this problem is\[P=5000 \times 1.15^\frac{ t }{ 10 }\]
anonymous
  • anonymous
then you plug in 30 for t
anonymous
  • anonymous
wat is the denominator under t?
anonymous
  • anonymous
lol the shortcut is easier and less complicated :P ur just jelly
anonymous
  • anonymous
nevermind, @HawkCrimson the shortcut you took doesn't work
anonymous
  • anonymous
D: haha
anonymous
  • anonymous
@Peter14 i dont understand...can you show me how it starts from P = Ae^(0.15t) ?
anonymous
  • anonymous
what you actually do each 10 years is you multiply the number of people by 1.15
anonymous
  • anonymous
cause it's 15%= . 15 right? :D
anonymous
  • anonymous
where does 1.15 come from?
anonymous
  • anonymous
oh ik how to do it by the shortcut way :P but it's long and tedius
anonymous
  • anonymous
1.15 is 115% the way the problem expresses this is as an exponential growth problem.
anonymous
  • anonymous
but the question says 15% :/
anonymous
  • anonymous
the shortcut you took would work for an arithmetic sequence (meaning you add a certain amount each time) but this is a geometric sequence (meaning you multiply by a certain amount each time.
anonymous
  • anonymous
lol forget me, answer the girl :P
anonymous
  • anonymous
100%=5000 pop so if it has a pop increase by 15% then it will become 115% that is y
anonymous
  • anonymous
the question says the population increases by 15% each time. The number you get shouldn't decrease at all. Let's look at the first case. If you multiply 5000 by 15% you get the increase in population: 750 people. You can then add that to 5000 to get 5750. or on the other hand, you can multiply 5000 by 115% (because 115% is 100%+15%) and that gives you 5750 with only one operation.
anonymous
  • anonymous
okay..
anonymous
  • anonymous
have you looked at compound interest in your math class or should I try to explain that to you?
anonymous
  • anonymous
how do i calculate using the formula dP/dt = kP ?
anonymous
  • anonymous
o.o where is that from?
anonymous
  • anonymous
try this http://qrc.depaul.edu/StudyGuide2009/Notes/Savings%20Accounts/Compound%20Interest.htm
anonymous
  • anonymous
its the formula given
anonymous
  • anonymous
what math class are you in?
anonymous
  • anonymous
i mean thats what we study in application of first order differential equations
anonymous
  • anonymous
from that formula we integrate and so on
anonymous
  • anonymous
wow, you've confused me.
anonymous
  • anonymous
XD
anonymous
  • anonymous
and google is sooo slow here in china so I have to stay confused...
anonymous
  • anonymous
ok, I understand now. you were given dP/dt = kP as the equation at the beginning. I get it.
anonymous
  • anonymous
what was the exact wording of the problem? I seem to have misunderstood it before.
anonymous
  • anonymous
i just want to know how do i start from P=Ae^(0.15t) from what i integrated from the above formula
anonymous
  • anonymous
what does A represent?
anonymous
  • anonymous
I think T would be 3, because it seems from the description at the top that T is in intervals of 10 years and then P looks like your final population
anonymous
  • anonymous
yeaa tried that but couldnt seem to get the answer right :/
anonymous
  • anonymous
http://fym.la.asu.edu/~pvaz/mat272/ch_07.pdf
anonymous
  • anonymous
wats the answer?
anonymous
  • anonymous
7604 people
anonymous
  • anonymous
you get that using the formula for compound interest, but I think they want you to show your work from using the methods they give you
anonymous
  • anonymous
i got that using the shortcut method but that wont get u any marks in the exam, ill try using the formulae
anonymous
  • anonymous
maybe you need to find the annual rate of increase instead of the rate of increase for 10 years
anonymous
  • anonymous
okay i'll try
anonymous
  • anonymous
P = Ae^0.15t P = 5000e^0.15(3) P = 7841 :/
anonymous
  • anonymous
do i have to find a new rate or what?
anonymous
  • anonymous
yes, you do and I know by doing some graphing tricks that the rate ends up approximately 0.013975, but I don't know exactly how you get that numerically. It should have something to do with ln something.
anonymous
  • anonymous
so in the textbook chapter you posted the final equation is P=A(e^kt) you are trying to find k given t=30 and a=5000 do they give you P? I guess what i'm trying to say is, what exactly do they give you at the start of the problem?
anonymous
  • anonymous
i got it! thanks guys for the help :)
anonymous
  • anonymous
I think you got it less because of us and more despite us.
anonymous
  • anonymous
but you guys made it more clear so thanks :D

Looking for something else?

Not the answer you are looking for? Search for more explanations.