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.)

Respuesta :

Answer:

96 people.

Step-by-step explanation:

Exponential equation for a decreasing amount:

The exponential equation for a decreasing amount is given by:

[tex]A(t) = A(0)(1-r)^t[/tex]

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 [tex]A(0) = 109[/tex]

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

This means that [tex]r = 0.03[/tex]

So

[tex]A(t) = A(0)(1-r)^t[/tex]

[tex]A(t) = 109(1-0.03)^t[/tex]

[tex]A(t) = 109(0.97)^t[/tex]

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

This is A(4). So

[tex]A(4) = 109(0.97)^4 = 96.49[/tex]

Rounding to the nearest whole number, 96 people.