# The population of Silver Run in the year 1890 was 6250. Assume the population increased at a rate of 2.75% per year. How do you estimate the population in 1915 and 1940?

Oct 8, 2016

12314 for 1915 and 24264 for 1940

#### Explanation:

If you were to do it a step at a time it would mean multiplying 6250 by 0.0275(2.75%), and adding the result to 6250, then repeating the operation with the new number for each year until you reached the amount of years required (25 and 50 years).

Now an easier way to do that first step would be multiplying by 1.0275, which already takes care of adding the original number. Now just do that for each of the intervals (25 and 50) required.

Now you can realize that:
$6250 \cdot 1.0275 \cdot 1.0275 \ldots \text{ " 25 " times is equal to } 6250 \cdot {1.0275}^{25}$

Then you can just plug that into your calculator, raise 1.0275 to the 25th (and then to the 50th) power and multiply that by 6250 and get your results.

$6250 \cdot {1.0275}^{25} = 12314$
$6250 \cdot {1.0275}^{50} = 24264$
Remember that both results are approximate as you can't have half a person.