A new shopping mall records 150 total shoppers on their first day of business. Each day after that, the number of shoppers is 15% more than the number of shoppers the day before. Which expression gives the total number of shoppers in the first n days of business? Choose 1 answer: (A) 1.15((1-150^(n))/(1-150)) (B) 0.85((1-150^(n))/(1-150)) (C) 150((1-1.15^(n))/(1-1.15)) (D) 150((1-0.85^(n))/(1-0.85))

Question

A new shopping mall records 150 total shoppers on their first day of business. Each day after that, the number of shoppers is  15% more than the number of shoppers the day before. Which expression gives the total number of shoppers in the first  n days of business? Choose 1 answer: (A)  1.15((1-150^(n))/(1-150)) (B)  0.85((1-150^(n))/(1-150)) (C)  150((1-1.15^(n))/(1-1.15)) (D)  150((1-0.85^(n))/(1-0.85))

Bytelearn · Accepted Answer

Understand the problem: Understand the problem. We need to find an expression that represents the total number of shoppers over the first n days, given that each day has 15% more shoppers than the previous day.Recognize the pattern: Recognize the pattern. The number of shoppers increases by a factor of 1.15 each day. This is a geometric sequence where the first term is 150 and the common ratio is 1.15.Write the formula: Write the formula for the sum of a geometric series. The sum S of the first n terms of a geometric series with first term a and common ratio r is given by S = a(1 - r^n) / (1 - r), provided r ≠ 1.Apply the formula: Apply the formula to the problem. In this case, a = 150 (the number of shoppers on the first day) and r = 1.15 (the growth factor). Plugging these values into the formula gives us S = 150(1 - 1.15^n) / (1 - 1.15).Check the answer choices: Check the answer choices. We need to find which option matches the expression we derived. Option (C) is 150((1-1.15^(n))/(1-1.15)), which is the correct expression for the sum of a geometric series with the given values.

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