A new shopping mall is gaining in popularity every day since it opened the number shoppers is 5% more than the number of shoppers the day before total number of shoppers over the first 10 days is 1258 how many shoppers were at the mall the first day

Question

Daniella Nolan

Mathematics

31 May, 02:01

A new shopping mall is gaining in popularity every day since it opened the number shoppers is 5% more than the number of shoppers the day before total number of shoppers over the first 10 days is 1258 how many shoppers were at the mall the first day

+4

Answers (1)

Know the Answer?

Dork · Answer 1

Step-by-step explanation:

The new shopping mall is gaining 5% more shoppers everyday than the number of shoppers the day before.

This means that for each day, the number of shoppers is 105% of the previous day. So the rate of increase is 105/100 = 1.05. This rate is in geometric progression. The formula for the sum of n terms of a geometric sequence is expressed as

Sn = a (r^n - 1) / r-1

Where

Sn is the total number of customers after n days

a is the number of shoppers at the mall the first day.

r is the rate or common ratio

n is the number of days

From the information given,

n = 10

Sn = S10 = 1258

r = 1.05

1258 = a (1.05^10 - 1) / 1.05-1

1258 = a * 0.63/0.05

1258 = 12.6a

a = 1258/12.6 = 99.84

The number of at the mall the first day is approximately 100 people