Question

Buffy's Beverages has increasing profits each week during the hot summer months. Buffy finds that each week during the summer his profits increase by 17% over what they were the previous week. In his first week of business, his profits were $334.

How much money will he make in all over 16 weeks?
please round your answer to the nearest cent

Answer 1

To solve this problem, we can use the formula for the sum of a geometric series:

S_n = a(1 - r^n)/(1 - r)

where S_n is the sum of the first n terms of the series, a is the first term, r is the common ratio, and n is the number of terms.

In this case, the first term is $334, the common ratio is 1.17 (since profits increase by 17% each week), and there are 16 terms (since we want to find the total profits over 16 weeks).

Plugging these values into the formula, we get:

S_16 = 334(1 - 1.17^16)/(1 - 1.17) ≈ $20,205.46

Therefore, Buffy's total profits over 16 weeks will be approximately $20,205.46.