Question

A new shopping mall is gaining in popularity. Every day since it opened, the number of shoppers is 20%, percent more than the number of shoppers the day before. The total number of shoppers over the first 4 days is 671.
How many shoppers were at the mall on the first day?
Round your final answer to the nearest integer.

Answer 1

Answer:

There were 125 shoppers on the first day.

Step-by-step explanation:

Let us call the number of shoppers on the first day $a_1$, then on the nth day the number of shoppers $a_n$ is

$a_n = a_1 (1.20)^{n-1}$

which is a geometric series whose sum to the nth term is

$\sum_{n=0}^{n-1} a_1(r^n) = a_1\dfrac{1-r^n}{1-r}$

Now, we know that the total number of shoppers over the first 4 days is 671; therefore,

$a_1\dfrac{1-r^n}{1-r^n} = 671$

$a_1\dfrac{1-(1.2)^4}{1-(1.2)} = 671$

$a_1(5.368) = 671$

$a_1 = \dfrac{671}{5.368}$

$\boxed{a_1 = 125 \;people. }$

Thus, there were 125 shoppers on the first day.