Problem:
From time t=0 to time t=1 a population increased by i%, and from time t=1 to time t=2 the population increased by j%. Therefore, from time t=0 to time t=2 the population increased by
Answer Choices:
A. (i+j)%
B. ij%
C. (i+ij)%
D. (i+j+100ij)%
E. (i+j+100i+j)%
Solution:
Let the population be P at time t=0, and suppose the population increased by k% from time t=0 to time t=2. The population at time t=2 is
P⋅(1+100k)=[P⋅(1+100i)](1+100j).
Hence
1+100k=1+100i+j+10000ij
so
k=i+j+100ij
Let i=j=100 to show that the other choices are not always correct.