Suppose a city with population 500,000 has been growing at a rate of ​6% per year. If this rate​ continues, find the population of this city in years.

Answer 1

We're trying to figure out the growth of something a a constant rate. In this case a city at 6% or .06.

We can take the original value, 500,000 and multiply it by .06 (500,000*.06) and we'll get 30,000. so after 1 year of growing at 6% our city will have 530,000 people.

What about year 2? We can take the new population value, 530,000 and multiply that by .06 and find out that 31,800 new people are in our city. We take 530,000 and add 31,800 to find out after 2 years we now have a population of 561,800.

We can keep doing that forever but there has to be an easier way right? There is!

Lets math it with some variables. Suppose p is the current population of the city. i is the growth rate, t is the time in years we're going to let it grow, and x is the population in the future after growing at rate i for t years.

We'd come up with something like: x = p*(1+i)^t

plugging our values in for 2 years; x = 500,000*(1+.06)^2 or 561,800

Cheers!