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.