Suppose the population of a town is 500,000 in 1990. The population increases at a rate of 5% every five years. What will be the population of the town in 2005?

Question

jim_thompson5910 · Answer

We now use the formula


A = P(1+r)^t


where P is the initial population, r is the rate of increase, and t is the amount of time


So now P = 500000, r = 0.05, and t = 15 (since 15 years elapse from 1990 to 2005)

jim_thompson5910 · Answer

So we can say


A = 500000(1+0.05)^15

anonymous · Answer

A= 500000(1.05)^15

jim_thompson5910 · Answer

so far so good

jim_thompson5910 · Answer

(1.05)^15 is what?

anonymous · Answer

2.07892818

jim_thompson5910 · Answer

good, so that means 


A= 500000(1.05)^15


becomes


A= 500000*2.07892818

jim_thompson5910 · Answer

then multiply that to get ...?

anonymous · Answer

$1,039,464

jim_thompson5910 · Answer

you have the right number (assuming you round to the nearest person), but no need for the $ sign (unless each person is a dollar lol)

anonymous · Answer

not to butt in, but it says 5% every five years. from 1990  to 2005 is 15 years, or 3 five year periods

jim_thompson5910 · Answer

oh good point, didn't see that satellite, thx for pointing that out

anonymous · Answer

yw

jim_thompson5910 · Answer

so it's really 


A = P(1+r)^(t/5)

jim_thompson5910 · Answer

so this means that 


A = P(1+r)^(t/5)


A = 500000(1+0.05)^(15/5)


A = 500000(1.05)^(15/5)


A = 500000(1.05)^3


A = 500000*1.157625


A = 578812.5


Telling us that the population will be about 578,812 people in the year 2005

anonymous · Answer

Wouln't it round to 578,813 because of the 0.5?

jim_thompson5910 · Answer

well I rounded down because that 0.5 represents a person that's not really there

anonymous · Answer

Oh! Haha, thats right, we are talking about people =) Thank you!

jim_thompson5910 · Answer

lol you're welcome