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:

Part (a)

Step1: Calculate population after first year

The initial population is 100. A 10% increase means we add 10% of 100 to 100. Mathematically, the population after the first year \( P_1=100 + 100\times0.1=100\times(1 + 0.1)=100\times1.1 = 110\).

Step2: Calculate population after second year

Now, we take the population after the first year (\(P_1 = 110\)) and increase it by 20%. A 20% increase on 110 means we calculate \(P_2=110+110\times0.2=110\times(1 + 0.2)=110\times1.2\).
Calculating \(110\times1.2 = 132\).

Percentage increases are applied to different bases. The 10% increase in the first year is based on the initial population of 100, and the 20% increase in the second year is based on the new population of 110 (after the first - year increase), not the original population of 100. So we can't just add the percentages (10%+20% = 30%) because the "whole" (the base of the percentage) changes after the first - year increase.

Answer:

The population after the second year is 132.

Part (b)