Question

Jacqueline owns a chain of fashion stores. She had 200 stores in 2010. Her goal is to increase the number of stores she owns at a rate of 20 percent every year.

If she sticks to her goal, in 2018 she will have approximately__stores.

Answer 1

Answer: 86


Step-by-step explanation:

This is a geometric series. This is, each year the number of stores is equal to the number of a store times a factor. And the factor is the same every year.

That lets you state this formula:

Number of stores year n = (number of stores year 1 ) × (factor) ⁿ

The year 1 is 2010.

The number of stores year 1 is 200 (given).

The factor is 1 + 20% = 1 + 0.20 = 1.20

In 2018, n = 2018 -2010 = 8.

So, you can subsitute all the values in the formula:

Number of stores year 8 = 200 (1,20)⁸ ≈ 85.99 ≈ 86