HELP WITH THIS ALGEBRA 2 QUESTION?

Question

The student population of Gloomy Valley High school has been steadily decreasing by 2% per year. If its population 8 years ago was 1200, which is the best expression for its population now?

 

A) 1200-1200(.02)^8

B) 1200(.98)^8

Answer 1

The general form of an exponential growth or decay equation is:

 

P = a(r)^t,

 

where t = time, a = initial amount, r = rate of growth or decay, and P = amount left after t time has gone by. You want the rate r to be equal to what percent of the previous year's population the current year's population is. If the population is declining by 2% each year, then each year 98% of the previous year's population remains. So, your answer is B, where 1200 is the initial amount, 0.98 is the rate of growth, and 8 is the time that has passed.