Answer:
There were 125 shoppers on the first day.
Step-by-step explanation:
Let us call the number of shoppers on the first day [tex]a_1[/tex], then on the nth day the number of shoppers [tex]a_n[/tex] is
[tex]a_n = a_1 (1.20)^{n-1}[/tex]
which is a geometric series whose sum to the nth term is
[tex]$\sum_{n=0}^{n-1} a_1(r^n) = a_1\dfrac{1-r^n}{1-r} $[/tex]
Now, we know that the total number of shoppers over the first 4 days is 671; therefore,
[tex]a_1\dfrac{1-r^n}{1-r^n} = 671 $[/tex]
[tex]a_1\dfrac{1-(1.2)^4}{1-(1.2)} = 671 $[/tex]
[tex]a_1(5.368) = 671 $[/tex]
[tex]a_1 = \dfrac{671}{5.368}[/tex]
[tex]\boxed{a_1 = 125 \;people. }[/tex]
Thus, there were 125 shoppers on the first day.
