The population of mastertown was 23,000 in 2012. assume that mastertowns population increased at a rate of 2% per year. write an equation to model the population of mastertown (y) based on a number of years since 2012(x).

Given:
2012 - 23,000 = base count
rate increase per year = 2%

y = 23,000 (1 + 0.02)^x

x is used as an exponent. 2012 will be 0. 0.02 is the decimal form of 2% increase.

2012 : y = 23,000 (1.02)⁰ = 23,000 (1) = 23,000
2013 : y = 23,000 (1.02)¹ = 23,000 (1.02) = 23,460
2014 : y = 23,000 (1.02)² = 23,000 (1.0404) = 23,929.20