Question

1. a herd of 100 caribou was moved to a new location. the population increased by 10% the first year and then increased by 20% the second year.

a) find the population after the second year.
b) explain why there was not a 30% increase in population over the two years.

Explanation:

Step1: Calculate year 1 population

Initial population: $100$. 10% increase: $100 + 100\times0.10 = 100\times1.10 = 110$

Step2: Calculate year 2 population

Year 1 population: $110$. 20% increase: $110 + 110\times0.20 = 110\times1.20 = 132$

b) The 20% increase in the second year is applied to the already increased population from the first year, not the original 100. A 30% total increase would only apply if both percentages were calculated from the initial population, but compound percentage growth uses the new population as the base each time.

Answer:

a) 132