A new shopping mall is gaining in popularity. Every day since it opened, the number of shoppers is 5%, percent more than the number of shoppers the day before. The total number of shoppers over the first 10 days is 1258.
How many shoppers were at the mall on the first day?

100 shoppers were at the mall on the first day.

Step-by-step explanation:

the number of shoppers is 5%, percent more than the number of shoppers the day before. It means that the number of shoppers is increasing in geometric sequence. The formula for determining the sum of n terms, Sn of a geometric sequence is expressed as

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

Where

n represents the number of term in the sequence.

a represents the first term in the sequence.

r represents the common ratio.

From the information given,

r = 1 + 5/100 = 1.05

n = 10

S10 = 1258

The expression for the sum of the first 10 term, S10 is

1258 = (a × 1.05^(10) - 1)/1.05 - 1

1258 = (a × 1.05^(10) - 1)/0.05

1258 = 0.628895a/0.05

1258 = 12.5779a

a = 1258/12.5779

a = 100