tasty treats finds that its profit from the sale of ice cream increeases by 5% per week during the 15-week summer season, Suppose the profit for the first week is $30. Determine the profit for the season.
2007-09-11 17:23:26 · 4 answers · asked by Anonymous in Science & Mathematics ➔ Mathematics
Since the profit increases by 5%, each profit is is 1.05 times the previous profit. So the net profit is
30 + 30(1.05) + 30(1.05)^2 + 30(1.05)^3 + ... 30(1.05)^14
This is a geometric series, not an arithmetic series where a = 30, r = 1.05 and n = 14.
2007-09-11 17:38:04 · answer #1 · answered by Anonymous · 0⤊ 0⤋
this is not an arithmetic series. It is a geometric series because each term is a product of the last one and 1.05
To = 30, r = 1.05
The formula for the sum of an geom series is
S = To (1-r^n)/(1-r)
= 30 (1-1.05)^30/(1-1.05)
= 647.36
2007-09-12 00:45:59 · answer #2 · answered by norman 7 · 0⤊ 0⤋
30, 31.50, 33.075 + .. This is a geometric series with r = 1.05
The sum is 30(1-1.05^15)(1-1.05)= $647.36
2007-09-12 00:38:31 · answer #3 · answered by ironduke8159 7 · 0⤊ 0⤋
$22.5
2007-09-12 00:34:05 · answer #4 · answered by lbelfer 4 · 0⤊ 1⤋