A city has a population of 370,000 people. Suppose that each year the population grows by 6.25%. What will the population be after 10 years?

Question

anonymous · Answer

OKAY! So i thought I got the hand of this but I DON'T :(

misty1212 · Answer

HI!!

misty1212 · Answer

same as the last one

misty1212 · Answer

what is $100\%+6.25\%$?

anonymous · Answer

The first problem we should look at deals with population growth.

If we look at what makes a population grow over one year maybe we can develop a model that will help us predict the future. 

Suppose that the population of a certain town is P is increasing at a constant rate of R each year. We can see that the population of our town one year later will be: 
P + P*R = P*( 1 + R )
Two years later the population of our town will be:
P*( 1 + R ) + (P*( 1 + R ))*R = P ( 1 + R ) ^ 2
So, in general the model of population growth looks like:

P*( 1 + R )^ (t-1) + (P*( 1 + R )^ (t-1))*R) = P*( 1 + R ) ^ t , where t is the number of years later.

misty1212 · Answer

??`

anonymous · Answer

106.25

misty1212 · Answer

ok good

misty1212 · Answer

so do $$370,000\times (1.0625)^{10}$$

anonymous · Answer

678408? I think I know what I've been doing wrong now..

misty1212 · Answer

probably put it in the calculator wrong is my guess

misty1212 · Answer

i would use this http://www.wolframalpha.com/input/?i=370000%281.0625%29%5E10

anonymous · Answer

How would I solve it if it was asking about decreasing rather than growing? @misty1212

misty1212 · Answer

decreasing by say $2\%$ the compute $100\%-2\%=98\%=.98$

anonymous · Answer

NOW I GET IT! THANKS <3