Question

A city has a population of 290,000 people. Suppose that each year the population grows by 5.25%. What will the population be after 10 years? Round your answer to the nearest whole number.

Answer 1

Basically Kelly, the plan for this problem would be as follows :)
290,000
x .0525
--------
Population. (we will call population P) So then, once you get P, you can add it back on to the original population, and multiply again 9 more times ;-;
I know there's a quicker way to do this, but im out of practice currently.

Ill get it going for you though!
fo the first year P = 15225
So then you'd do 290,000 + 15225 = 305225.
Repeat

Answer 2

I'm not really understanding. @YoloShroom

Answer 3

@zepdrix

Answer 4

It's no problem, ill explain it slowly so you do :)

Answer 5

So the population of the city is 290,000 people correct?
We know the population growth of the city is .0525 (or 5.25%) each year.
we want to find out the population after 10 years.

Answer 6

right?

Answer 7

Yes.

Answer 8

Alright so, to find the "Increase" in population after one year, we need to multiply the current population (290,000) by the increase percentage (.0525).
So 290,000 x .0525 = 15225.

Answer 9

15,225 is the amount of increase in one year.
so we can add that on to the original population amount of 290,000.
so 290,000+15,225 = 305,225.

Here we see that 305,225 is the population after one year of increase.

Answer 10

does that make more sense?

Answer 11

please remember that this isnt the final answer.

Answer 12

This can be modeled by \[y=290000(1.0525)^x\] Where y is the total population and x is the years gone by

Answer 13

So by substituting 10 you could get the answer an easier way

Answer 14

Ofc you could ^_^ but we dont know to what extent Kelly understands exponents ^^