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shaqadry
 2 years 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?
shaqadry
 2 years 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
 2 years ago
Best ResponseYou've already chosen the best response.0have any ideas wat to do? :)

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

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

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

HawkCrimson
 2 years 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
 2 years 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
 2 years ago
Best ResponseYou've already chosen the best response.1then you plug in 30 for t

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

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

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

shaqadry
 2 years 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
 2 years 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
 2 years ago
Best ResponseYou've already chosen the best response.0cause it's 15%= . 15 right? :D

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

HawkCrimson
 2 years 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
 2 years 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
 2 years ago
Best ResponseYou've already chosen the best response.1but the question says 15% :/

Peter14
 2 years 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
 2 years ago
Best ResponseYou've already chosen the best response.0lol forget me, answer the girl :P

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

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

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

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

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

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

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

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

Peter14
 2 years 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
 2 years 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
 2 years 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
 2 years 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
 2 years ago
Best ResponseYou've already chosen the best response.1yeaa tried that but couldnt seem to get the answer right :/

Peter14
 2 years 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
 2 years 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
 2 years 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
 2 years ago
Best ResponseYou've already chosen the best response.0P = Ae^0.15t P = 5000e^0.15(3) P = 7841 :/

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

Peter14
 2 years 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
 2 years 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
 2 years ago
Best ResponseYou've already chosen the best response.1i got it! thanks guys for the help :)

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

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