Asmall country in europe has been experiencing population growth that can be modeled by the equation y=120,000(1.042)^x where y is the population of the country and x is the number of years since 2010. what is the percent change in the population of the country each year?

This is a super long answer, you just need to ready the first paragraph but if you would like to understand it better you can read the whole thing. The percentage change in the population each year is 4.2%. 120,000 is the population of the country at the start of 2010- this is called the Principal or 'P'.  The 1.042 in brackets is the percentage rise of the population. 1 in the decimal stands for the 120,000 initial population, .042 stands for the growth in the population. So by saying y=120,000(1.042) you are basically multiplying the 120,000 by 1 and adding on 4.2%.

Now that we have y=120,000(1.042) we need to multiply the whole equation by 'x'' because x is the number of years that the population rose by that percent. 
Lets say that x=1. Y would be the population 120,000 multiplied by 1.042. And then that answer would be put to the power of 1 (multiplied by 1) giving the rise in population over one year. If someone were to want to know what the rise of the population would be in two years, they have to tweak the equation so that x= 2. If they wanted to see a rise in 3 year it would be x=3.