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: choose 1 answer: (choice a) \[1.15\left(\dfrac{1-150^n}{1-150}\right)\] a \[1.15\left(\dfrac{1-150^n}{1-150}\right)\] (choice b) \[0.85\left(\dfrac{1-150^n}{1-150}\right)\] b \[0.85\left(\dfrac{1-150^n}{1-150}\right)\] (choice c) \[150\left(\dfrac{1-1.15^n}{1-1.15}\right)\] c \[150\left(\dfrac{1-1.15^n}{1-1.15}\right)\] (choice d) \[150\left(\dfrac{1-0.85^n}{1-0.85}\right)\] d \[150\left(\dfrac{1-0.85^n}{1-0.85}\right)\]\

Answer 1

The total number of shoppers in the first n days of business, with a 15% daily increase, is given by the formula 150 * (1 - 1.15^n) / (1 - 1.15), which is choice (C).

Step-by-step explanation:

The correct expression to find the total number of shoppers in the first n days when the number of shoppers increases by 15% each day is given by a geometric series sum formula.

On the first day, there are 150 shoppers, and each subsequent day sees a 15% increase; hence, we can model this as 150, 150(1.15), 150(1.15)^2, ..., 150(1.15)^(n-1).

The sum of the first n terms of a geometric series is given by the formula S = a(1 - r^n) / (1 - r), where a is the first term and r is the common ratio.

Here, the first term a is 150, and the common ratio r is 1.15 since the number of shoppers is increasing by 15% every day.

Therefore, the total number of shoppers over the n days is given by 150 * (1 - 1.15^n) / (1 - 1.15), which corresponds to choice (C).