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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))

A new shopping mall records 150150 total shoppers on their first day of business. Each day after that, the number of shoppers is 15% 15 \% more than the number of shoppers the day before.\newlineWhich expression gives the total number of shoppers in the first n n days of business?\newlineChoose 11 answer:\newline(A) 1.15(1−150n1−150) 1.15\left(\frac{1-150^{n}}{1-150}\right) \newline(B) 0.85(1−150n1−150) 0.85\left(\frac{1-150^{n}}{1-150}\right) \newline(C) 150(1−1.15n1−1.15) 150\left(\frac{1-1.15^{n}}{1-1.15}\right) \newline(D) 150(1−0.85n1−0.85) 150\left(\frac{1-0.85^{n}}{1-0.85}\right)

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Q. A new shopping mall records 150150 total shoppers on their first day of business. Each day after that, the number of shoppers is 15% 15 \% more than the number of shoppers the day before.\newlineWhich expression gives the total number of shoppers in the first n n days of business?\newlineChoose 11 answer:\newline(A) 1.15(1−150n1−150) 1.15\left(\frac{1-150^{n}}{1-150}\right) \newline(B) 0.85(1−150n1−150) 0.85\left(\frac{1-150^{n}}{1-150}\right) \newline(C) 150(1−1.15n1−1.15) 150\left(\frac{1-1.15^{n}}{1-1.15}\right) \newline(D) 150(1−0.85n1−0.85) 150\left(\frac{1-0.85^{n}}{1-0.85}\right)
  1. Understand the problem: Understand the problem.\newlineWe need to find an expression that represents the total number of shoppers in the first nn days, given that each day has 15%15\% more shoppers than the previous day.
  2. Recognize the pattern: Recognize the pattern.\newlineThe number of shoppers increases by a factor of 1.151.15 each day. This is a geometric sequence where the first term (a1)(a_1) is 150150 and the common ratio (r)(r) is 1.151.15.
  3. Write the formula: Write the formula for the sum of the first nn terms of a geometric sequence.\newlineThe sum SnS_n of the first nn terms of a geometric sequence is given by the formula:\newlineSn=a1×(1−rn)/(1−r)S_n = a_1 \times (1 - r^n) / (1 - r), where a1a_1 is the first term and rr is the common ratio.
  4. Plug in values: Plug in the values for a1a_1 and rr into the formula.\newlineIn this case, a1=150a_1 = 150 (the number of shoppers on the first day) and r=1.15r = 1.15 (the daily increase factor).\newlineSo, the expression for the total number of shoppers over nn days is:\newlineSn=150×(1−1.15n)/(1−1.15)S_n = 150 \times (1 - 1.15^n) / (1 - 1.15)
  5. Simplify the expression: Simplify the expression.\newlineThe expression simplifies to:\newlineSn=150×(1−1.15n)/(1−1.15)S_n = 150 \times (1 - 1.15^n) / (1 - 1.15)\newlineThis matches option (C) from the given choices.

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