Problem: The yearly changes in the population census of a town for four consecutive years are, respectively, 25% increase, 25% increase, 25% decrease, 25% decrease. The net change over the four years, to the nearest percent, is:
Answer Choices:
A. −12
B. −1
C. 0
D. 1
E. 12
Solution:
Let P be the original population. Then,
after 1 year the.population is 1.25P
after 2 years the population is (1.25)(1.25)p
after 3 years the population is (1.25)(1.25)(.75)P
after 4 years the population is (1.25)(1.25)(.75)(.75)P=225/256P
The net percent change is P225/256P−P​×100
=P0.88P−P​×100=−12.