Between 1980 and 1990 a small town's population increased from 10000 to 12500. Between 1990 and 2000 its population increased from 12500 to 14500. By what percent did the rate of population growth decrease from the period 1980-1990 to the period 1990-2000?
Pick one:
A) 20%
B) 24%
C) 28%
D) 32%
E) 36%
Solution:   This is a percent decrease problem. We will use the formula: percent change = (new – old)/old x 100 to calculate the final answer.   We first set up the ratios of population growth to initial population for the two periods. The first ratio will be for the period 1980-1990, and the second ratio will be for the period 1990-2000. Because the populations are in hundreds, we do not have to express all the trailing zeros in our ratios.   1980-1990   growth/initial population = 2500/10000 = 1/4   1990-2000   growth/initial population = 2000/12500 = 4/25   Because each ratio is not an easy number to use, we can simplify each one by multiplying each by the LCM of the two denominators, which is 100. Keep in mind that we are able to do this only because our answer choices are expressed in percents.   1980-1990   growth/initial population = (1/4) x 100 = 25   1990-2000   growth/initial population = (4/25) x 100 = 16   We can plug 25 and 16 into our percent change formula:   (new – old)/old x 100   [(16 – 25)/25] x 100   -9/25 x 100   At this point we can stop and consider the answer choices. -9/25 x 100 is -36, so the decrease is by 36%.   Answer 36%.
<result>E</result>
Between 1980 and 1990 a small town's population increased from 10000 to 12500. Between 1990 and 2000 its population increased from 12500 to 14500. By what percent did the rate of population growth decrease from the period 1980-1990 to the period 1990-2000?