Question

Currently, the number of people entering a shopping mall is 109. It is estimated that the number of people entering the shopping mall will decrease by 3% each hour. Find the total number of people entering the shopping mall at the end of 4 hours. (Round your answer to the nearest whole number if necessary.)

Answer 1

96 people.

Explanation:

Exponential equation for a decreasing amount:

The exponential equation for a decreasing amount is given by:

`A(t) = A(0)(1-r)^t`

In which A(0) is the initial rate and r is the decay rate, as a decimal.

Currently, the number of people entering a shopping mall is 109.

This means that
`A(0) = 109`

It is estimated that the number of people entering the shopping mall will decrease by 3% each hour.

This means that
`r = 0.03`

So

`A(t) = A(0)(1-r)^t`

`A(t) = 109(1-0.03)^t`

`A(t) = 109(0.97)^t`

Find the total number of people entering the shopping mall at the end of 4 hours.

This is A(4). So

`A(4) = 109(0.97)^4 = 96.49`

Rounding to the nearest whole number, 96 people.