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

Answer:

96 people.

Step-by-step 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.