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
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
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.
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