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 one year ago
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?
 one year ago
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?

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HawkCrimson
 one year ago
Best ResponseYou've already chosen the best response.0have any ideas wat to do? :)

HawkCrimson
 one year ago
Best ResponseYou've already chosen the best response.0or how to start off?

Peter14
 one year ago
Best ResponseYou've already chosen the best response.1do you know an equation that works for this kind of thing?

shaqadry
 one year ago
Best ResponseYou've already chosen the best response.1yes. i work it out until i got P = Ae^(0.15t)

HawkCrimson
 one year ago
Best ResponseYou've already chosen the best response.0since 10yrs=15% then 30yrs=45% thus the population growth in 30 yrs is 5000 x 145/100 50 x 145

Peter14
 one year ago
Best ResponseYou've already chosen the best response.1the equation you can find for this problem is\[P=5000 \times 1.15^\frac{ t }{ 10 }\]

Peter14
 one year ago
Best ResponseYou've already chosen the best response.1then you plug in 30 for t

HawkCrimson
 one year ago
Best ResponseYou've already chosen the best response.0wat is the denominator under t?

HawkCrimson
 one year ago
Best ResponseYou've already chosen the best response.0lol the shortcut is easier and less complicated :P ur just jelly

Peter14
 one year ago
Best ResponseYou've already chosen the best response.1nevermind, @HawkCrimson the shortcut you took doesn't work

shaqadry
 one year ago
Best ResponseYou've already chosen the best response.1@Peter14 i dont understand...can you show me how it starts from P = Ae^(0.15t) ?

Peter14
 one year ago
Best ResponseYou've already chosen the best response.1what you actually do each 10 years is you multiply the number of people by 1.15

HawkCrimson
 one year ago
Best ResponseYou've already chosen the best response.0cause it's 15%= . 15 right? :D

shaqadry
 one year ago
Best ResponseYou've already chosen the best response.1where does 1.15 come from?

HawkCrimson
 one year ago
Best ResponseYou've already chosen the best response.0oh ik how to do it by the shortcut way :P but it's long and tedius

Peter14
 one year ago
Best ResponseYou've already chosen the best response.11.15 is 115% the way the problem expresses this is as an exponential growth problem.

shaqadry
 one year ago
Best ResponseYou've already chosen the best response.1but the question says 15% :/

Peter14
 one year ago
Best ResponseYou've already chosen the best response.1the 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.

HawkCrimson
 one year ago
Best ResponseYou've already chosen the best response.0lol forget me, answer the girl :P

HawkCrimson
 one year ago
Best ResponseYou've already chosen the best response.0100%=5000 pop so if it has a pop increase by 15% then it will become 115% that is y

Peter14
 one year ago
Best ResponseYou've already chosen the best response.1the 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.

Peter14
 one year ago
Best ResponseYou've already chosen the best response.1have you looked at compound interest in your math class or should I try to explain that to you?

shaqadry
 one year ago
Best ResponseYou've already chosen the best response.1how do i calculate using the formula dP/dt = kP ?

Peter14
 one year ago
Best ResponseYou've already chosen the best response.1o.o where is that from?

Peter14
 one year ago
Best ResponseYou've already chosen the best response.1try this http://qrc.depaul.edu/StudyGuide2009/Notes/Savings%20Accounts/Compound%20Interest.htm

shaqadry
 one year ago
Best ResponseYou've already chosen the best response.1its the formula given

Peter14
 one year ago
Best ResponseYou've already chosen the best response.1what math class are you in?

shaqadry
 one year ago
Best ResponseYou've already chosen the best response.1i mean thats what we study in application of first order differential equations

shaqadry
 one year ago
Best ResponseYou've already chosen the best response.1from that formula we integrate and so on

Peter14
 one year ago
Best ResponseYou've already chosen the best response.1wow, you've confused me.

Peter14
 one year ago
Best ResponseYou've already chosen the best response.1and google is sooo slow here in china so I have to stay confused...

Peter14
 one year ago
Best ResponseYou've already chosen the best response.1ok, I understand now. you were given dP/dt = kP as the equation at the beginning. I get it.

Peter14
 one year ago
Best ResponseYou've already chosen the best response.1what was the exact wording of the problem? I seem to have misunderstood it before.

shaqadry
 one year ago
Best ResponseYou've already chosen the best response.1i just want to know how do i start from P=Ae^(0.15t) from what i integrated from the above formula

Peter14
 one year ago
Best ResponseYou've already chosen the best response.1what does A represent?

Peter14
 one year ago
Best ResponseYou've already chosen the best response.1I 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

shaqadry
 one year ago
Best ResponseYou've already chosen the best response.1yeaa tried that but couldnt seem to get the answer right :/

Peter14
 one year ago
Best ResponseYou've already chosen the best response.1you 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

HawkCrimson
 one year ago
Best ResponseYou've already chosen the best response.0i got that using the shortcut method but that wont get u any marks in the exam, ill try using the formulae

Peter14
 one year ago
Best ResponseYou've already chosen the best response.1maybe you need to find the annual rate of increase instead of the rate of increase for 10 years

HawkCrimson
 one year ago
Best ResponseYou've already chosen the best response.0P = Ae^0.15t P = 5000e^0.15(3) P = 7841 :/

shaqadry
 one year ago
Best ResponseYou've already chosen the best response.1do i have to find a new rate or what?

Peter14
 one year ago
Best ResponseYou've already chosen the best response.1yes, 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.

Peter14
 one year ago
Best ResponseYou've already chosen the best response.1so 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?

shaqadry
 one year ago
Best ResponseYou've already chosen the best response.1i got it! thanks guys for the help :)

Peter14
 one year ago
Best ResponseYou've already chosen the best response.1I think you got it less because of us and more despite us.

shaqadry
 one year ago
Best ResponseYou've already chosen the best response.1but you guys made it more clear so thanks :D
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