Answer :
To solve this problem, let's break down the steps:
1. Understand the Decrease in Sales:
The problem states that the windshield wiper sales decrease at a rate of 4.5% per month. This means that each month, the store sells 4.5% less than the previous month.
2. Calculate the Remaining Percentage Sold Each Month:
If sales decrease by 4.5%, then 100% - 4.5% = 95.5% of the previous month's sales are sold each month. This can be represented as a decimal: 0.955.
3. Determine the Exponential Function:
We know that initially, 124 pairs of windshield wipers were sold in April. We're looking for a function that shows the decrease over multiple months.
4. Set Up the Function:
Since the sales decrease is exponential (a consistent percentage decrease each month), we use an exponential decay function. The number of windshield wipers sold [tex]\( m \)[/tex] months after April can be represented by the function:
[tex]\[
w(m) = 124 \times (0.955)^m
\][/tex]
Here, 124 is the initial number of sales, 0.955 is the remaining sales rate after each month, and [tex]\( m \)[/tex] is the number of months after April.
This procedure results in the function:
[tex]\[ w(m) = 124(0.955)^m \][/tex]
This function correctly models the continuous monthly decrease in sales, reflecting the initial condition and the monthly percentage decrease.
1. Understand the Decrease in Sales:
The problem states that the windshield wiper sales decrease at a rate of 4.5% per month. This means that each month, the store sells 4.5% less than the previous month.
2. Calculate the Remaining Percentage Sold Each Month:
If sales decrease by 4.5%, then 100% - 4.5% = 95.5% of the previous month's sales are sold each month. This can be represented as a decimal: 0.955.
3. Determine the Exponential Function:
We know that initially, 124 pairs of windshield wipers were sold in April. We're looking for a function that shows the decrease over multiple months.
4. Set Up the Function:
Since the sales decrease is exponential (a consistent percentage decrease each month), we use an exponential decay function. The number of windshield wipers sold [tex]\( m \)[/tex] months after April can be represented by the function:
[tex]\[
w(m) = 124 \times (0.955)^m
\][/tex]
Here, 124 is the initial number of sales, 0.955 is the remaining sales rate after each month, and [tex]\( m \)[/tex] is the number of months after April.
This procedure results in the function:
[tex]\[ w(m) = 124(0.955)^m \][/tex]
This function correctly models the continuous monthly decrease in sales, reflecting the initial condition and the monthly percentage decrease.
