Answer :
To determine the charges for different distances traveled by a cab according to the given rate chart, let's follow the steps listed below.
### Rate Chart Explanation
1. Flag Drop Fee: There is an initial charge of [tex]$5.00, which is applicable even if no distance is traveled. 2. Rate for 0 to 10 Miles: For distances from 0 to less than 10 miles, an additional $[/tex]1.00 per mile is charged on top of the flag drop fee.
3. Rate for Over 10 Miles: For distances equal to or more than 10 miles, the rate changes. The charge is [tex]$1.00 per mile for the first 10 miles, and $[/tex]2.00 per mile for miles beyond 10.
### Calculating Charges at Specific Distances
We will calculate the charges for five example distances: 0 miles, 5 miles, 10 miles, 15 miles, and 20 miles.
#### 1. Distance: 0 miles
- Initial flag drop fee: [tex]$5.00 - Miles traveled: 0 mile × $[/tex]1.00/mile = [tex]$0.00 - Total Charge: $[/tex]5.00 + [tex]$0.00 = $[/tex]5.00
#### 2. Distance: 5 miles
- Initial flag drop fee: [tex]$5.00 - Miles traveled: 5 miles × $[/tex]1.00/mile = [tex]$5.00 - Total Charge: $[/tex]5.00 + [tex]$5.00 = $[/tex]10.00
#### 3. Distance: 10 miles
- Initial flag drop fee: [tex]$5.00 - Miles traveled: 10 miles × $[/tex]1.00/mile = [tex]$10.00 - Total Charge: $[/tex]5.00 + [tex]$10.00 = $[/tex]15.00
#### 4. Distance: 15 miles
- Initial flag drop fee: [tex]$5.00 - First 10 miles: 10 miles × $[/tex]1.00/mile = [tex]$10.00 - Additional 5 miles: 5 miles × $[/tex]2.00/mile = [tex]$10.00 - Total Charge: $[/tex]5.00 + [tex]$10.00 + $[/tex]10.00 = [tex]$25.00 #### 5. Distance: 20 miles - Initial flag drop fee: $[/tex]5.00
- First 10 miles: 10 miles × [tex]$1.00/mile = $[/tex]10.00
- Additional 10 miles: 10 miles × [tex]$2.00/mile = $[/tex]20.00
- Total Charge: [tex]$5.00 + $[/tex]10.00 + [tex]$20.00 = $[/tex]35.00
### Summary of Charges
The charges for the distances 0, 5, 10, 15, and 20 miles are:
- 0 miles: [tex]$5.00 - 5 miles: $[/tex]10.00
- 10 miles: [tex]$15.00 - 15 miles: $[/tex]25.00
- 20 miles: [tex]$35.00 These charges can be graphically represented as points on a graph where the x-axis represents the distance in miles, and the y-axis represents the total charge in dollars. ### Visual Representation - At 0 miles, point (0, 5) - At 5 miles, point (5, 10) - At 10 miles, point (10, 15) - At 15 miles, point (15, 25) - At 20 miles, point (20, 35) These points should appear as a piecewise linear graph, with the first segment from (0, 5) to (10, 15) showing a gentler slope (rate $[/tex]1.00 per mile) and the second segment from (10, 15) to (20, 35) being steeper (rate $2.00 per mile beyond 10 miles).
### Rate Chart Explanation
1. Flag Drop Fee: There is an initial charge of [tex]$5.00, which is applicable even if no distance is traveled. 2. Rate for 0 to 10 Miles: For distances from 0 to less than 10 miles, an additional $[/tex]1.00 per mile is charged on top of the flag drop fee.
3. Rate for Over 10 Miles: For distances equal to or more than 10 miles, the rate changes. The charge is [tex]$1.00 per mile for the first 10 miles, and $[/tex]2.00 per mile for miles beyond 10.
### Calculating Charges at Specific Distances
We will calculate the charges for five example distances: 0 miles, 5 miles, 10 miles, 15 miles, and 20 miles.
#### 1. Distance: 0 miles
- Initial flag drop fee: [tex]$5.00 - Miles traveled: 0 mile × $[/tex]1.00/mile = [tex]$0.00 - Total Charge: $[/tex]5.00 + [tex]$0.00 = $[/tex]5.00
#### 2. Distance: 5 miles
- Initial flag drop fee: [tex]$5.00 - Miles traveled: 5 miles × $[/tex]1.00/mile = [tex]$5.00 - Total Charge: $[/tex]5.00 + [tex]$5.00 = $[/tex]10.00
#### 3. Distance: 10 miles
- Initial flag drop fee: [tex]$5.00 - Miles traveled: 10 miles × $[/tex]1.00/mile = [tex]$10.00 - Total Charge: $[/tex]5.00 + [tex]$10.00 = $[/tex]15.00
#### 4. Distance: 15 miles
- Initial flag drop fee: [tex]$5.00 - First 10 miles: 10 miles × $[/tex]1.00/mile = [tex]$10.00 - Additional 5 miles: 5 miles × $[/tex]2.00/mile = [tex]$10.00 - Total Charge: $[/tex]5.00 + [tex]$10.00 + $[/tex]10.00 = [tex]$25.00 #### 5. Distance: 20 miles - Initial flag drop fee: $[/tex]5.00
- First 10 miles: 10 miles × [tex]$1.00/mile = $[/tex]10.00
- Additional 10 miles: 10 miles × [tex]$2.00/mile = $[/tex]20.00
- Total Charge: [tex]$5.00 + $[/tex]10.00 + [tex]$20.00 = $[/tex]35.00
### Summary of Charges
The charges for the distances 0, 5, 10, 15, and 20 miles are:
- 0 miles: [tex]$5.00 - 5 miles: $[/tex]10.00
- 10 miles: [tex]$15.00 - 15 miles: $[/tex]25.00
- 20 miles: [tex]$35.00 These charges can be graphically represented as points on a graph where the x-axis represents the distance in miles, and the y-axis represents the total charge in dollars. ### Visual Representation - At 0 miles, point (0, 5) - At 5 miles, point (5, 10) - At 10 miles, point (10, 15) - At 15 miles, point (15, 25) - At 20 miles, point (20, 35) These points should appear as a piecewise linear graph, with the first segment from (0, 5) to (10, 15) showing a gentler slope (rate $[/tex]1.00 per mile) and the second segment from (10, 15) to (20, 35) being steeper (rate $2.00 per mile beyond 10 miles).
