The population of a city in 2005 was 18,000. by 2010, the city’s population had grown to 45,000. economists have determined that the population growth follows an exponential model. if they are correct, what is the projected population for 2015?

2005= 18,000
2010= 45,000

1) make 2005 year "0", and 2010 year "5"
2)in order to solve this problem and figure out the rate of change, we must use the equation for exponential functions y=ab^x
3) a= the y- value of y intercept ( what does y equal when x is zero) in this case a population number so, a= 18,000; b= the unknown rate of change; x= time and since we're finding  b we can plug in 5 for the time in years; y= the value of y in terms of the x-value, so when x is 5, y is 45,000
4) you end up with something like this
45,000= 18,000b^5
5) in order to proceed to solve you must get b alone
6) divide both sides by 18,000
7) so you no have 2.5= b^5
8) take the fifth root of both sides 
9) now you have your answer b=1.20112443398