Question

Pat has a lawn mowing business and has been experimenting with different prices in order to earn the most money. Some of the prices he has tried are listed in the table below. Week Price # of lawns 1 $20.00 2 2 $17.00 7 3 $13.00 18 4 $10.50 33 Write an equation to model the price for a given week if Pat keeps lowering the price at about the same rate. Write a similar equation to model the number of customers per week if the number of customers continues to increase in a similar way. When would Pat achieve the highest revenue?

Answer 1

The data are
Week   Price      # of lawns
1          $20.00   2
2          $17.00   7 
3          $13.00   18
4          $10.50   33
The equation that models the week number and price is
y = -3.25x + 23.25
where x is the week number
y is the price