Final answer:
To determine the total number of shoppers over the first 7 days, a geometric progression was used, with each day seeing a 10% increase in shoppers from the previous day, starting with 120. After calculating the number of shoppers for each day and summing those numbers, we found that approximately 1140 shoppers visited the mall in 7 days.
Step-by-step explanation:
To calculate the total number of shoppers that visited the mall in the first 7 days, we will use the concept of geometric sequences where each term increases by a constant percentage from the previous one. The first day had 120 shoppers, and each subsequent day saw a 10% increase in shoppers. This can be represented by the formula:
Total shoppers = first day shoppers × (1 + rate of increase)number of days
In this case:
Total shoppers = 120 × (1 + 0.10)n, where n is the day number.
We will calculate this for each day from day 1 to day 7 and sum the totals:
- Day 1: 120
- Day 2: 120 × 1.10
- Day 3: 120 × 1.102
- Day 4: 120 × 1.103
- Day 5: 120 × 1.104
- Day 6: 120 × 1.105
- Day 7: 120 × 1.106
Summing up all these values, and rounding to the nearest integer, we get the total number of shoppers over the 7 days.
Let's compute the exact values:
- Day 1: 120 shoppers
- Day 2: 120 × 1.10 = 132 shoppers
- Day 3: 120 × 1.102 ≈ 145 shoppers
- Day 4: 120 × 1.103 ≈ 160 shoppers
- Day 5: 120 × 1.104 ≈ 176 shoppers
- Day 6: 120 × 1.105 ≈ 194 shoppers
- Day 7: 120 × 1.106 ≈ 213 shoppers
Adding all these values gives us:
Total = 120 + 132 + 145 + 160 + 176 + 194 + 213 = 1140 shoppers over the 7 days.