Question

A new shopping mall records 120 total shoppers on their first day of business. Each day after that, the number of shoppers is 10, percent more than the number of shoppers the day before. What is the total number of shoppers that visited the mall in the first 7 days?

Answer 1

1138

Explanation:

From the information given:

We can represent it perfectly in an exponential form:

`m = p(q)^x`

where;

p = initial value = 120

q = base of the exponential form

q = 1 + r

here; r = rate in decimal = 10% = 0.1

Then q can now be = 1 + 0.1 = 1.1

Replacing it into the exponential form, we get:

`m = 120(1.1)^x`

where;

x = number of days and m = number of shoppers

Thus:

For the first day:

`m = 120(1.1)^x`

m = 120

For the second day:

`m = 120(1.1)^1`

m = 132

For the third day:

`m = 120(1.1)^2`

m = 145.2

For the fourth day

`m = 120(1.1)^3`

m = 159.72

For the fifth-day

`m = 120(1.1)^4`

m = 175.692

For the sixth-day

`m = 120(1.1)^5`

m = 193.2612

For the seventh-day

`m = 120(1.1)^6`

m = 212.58732

Thus; the total numbers of shoppers for the first 7 days is:

`= 120+ 132 + 145.2 + 159.72 + 175.692+193.2612+212.58732`

= 1138.46052

≅ 1138