​According to the following graph, find the average annual percentage growth of mascara through the years 2001, 2002, 2003 and 2004.​

Correct option is D

Given:

Sales of Mascara (from the graph):

2001: 2 (in hundreds, or 200 units)

2004: 6 (in hundreds, or 600 units)

Number of years (n): From 2001 to 2004 = 3 years.

Concept Used:

The Compound Annual Growth Rate (CAGR) formula is used to find the average annual percentage growth rate over a period.

The formula is:

​$$CAGR = \left( \frac{\text{Final Value}}{\text{Initial Value}} \right)^{\frac{1}{n}} - 1$$ 

Solution:

Substitute the values into the formula:

​$$CAGR = \left( \frac{600}{200} \right)^{\frac{1}{3}} - 1$$ 

$$= \left( 3 \right)^{\frac{1}{3}} - 1$$ 

The cube root of 3 is approximately 1.46.

​$$CAGR=1.46−1=0.46$$ 

$$CAGR=0.46×100=46\%$$ 

Thus the average annual percentage growth of mascara sales from 2001 to 2004 is 46%.