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A new shopping mall is gaining in popularity. Every day since it opened, the number of shoppers is
20% 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.
shoppers

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

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Exponential growth and decay: word problems

Full solution

Q. A new shopping mall is gaining in popularity. Every day since it opened, the number of shoppers is

20 \%

more than the number of shoppers the day before. The total number of shoppers over the first

4

days is

671

.

\newline

How many shoppers were at the mall on the first day?

\newline

Round your final answer to the nearest integer.

\newline

shoppers

Denote Shoppers: Let's denote the number of shoppers on the first day as $S$ . Since the number of shoppers increases by $20$ % each day, the number of shoppers on the second day would be $S \times 1.20$ , on the third day $S \times 1.20^2$ , and on the fourth day $S \times 1.20^3$ . We are given that the total number of shoppers over the first $4$ days is $671$ . We can set up the following equation to represent this information: $\newline$ $S + S \times 1.20 + S \times 1.20^2 + S \times 1.20^3 = 671$
Set Up Equation: First, factor out $S$ from the left side of the equation: $\newline$ $S(1 + 1.20 + 1.20^2 + 1.20^3) = 671$ $\newline$ Now calculate the sum within the parentheses: $\newline$ $1 + 1.20 + 1.20^2 + 1.20^3 = 1 + 1.20 + 1.44 + 1.728$ $\newline$ $1 + 1.20 + 1.44 + 1.728 = 5.368$ $\newline$ So the equation simplifies to: $\newline$ $S \times 5.368 = 671$
Factor Out S: Now, divide both sides of the equation by $5$ . $368$ to solve for $S$ : $\newline$ $S = \frac{671}{5.368}$ $\newline$ $S \approx 125.046$ $\newline$ Since we need to round the final answer to the nearest integer, we round $125$ . $046$ to $125$ .

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