Lewis works at a bookstore where he earns $8.25/h. a) Create a table of values to show his total earnings for up to 6 hours of work. b) Determine the rate of change in Lewis's tota... Lewis works at a bookstore where he earns $8.25/h. a) Create a table of values to show his total earnings for up to 6 hours of work. b) Determine the rate of change in Lewis's total earnings. c) Graph your table of values. Connect the points with a straight line.
Understand the Problem
The question is asking to calculate Lewis's total earnings based on his hourly wage and to create a table and graph for these earnings over a range of hours worked.
Answer
Total earnings for Lewis are $E = 8.25h$ with earnings of $49.50$ after $6$ hours of work. The rate of change is $8.25$ per hour.
Answer for screen readers
Lewis's total earnings after working up to 6 hours are:
- 0 hours: $0
- 1 hour: $8.25
- 2 hours: $16.50
- 3 hours: $24.75
- 4 hours: $33.00
- 5 hours: $41.25
- 6 hours: $49.50
The rate of change in Lewis's total earnings is $8.25 per hour.
Steps to Solve
- Calculate total earnings for each hour worked
Lewis earns $8.25 per hour. To determine his total earnings for various hours worked, multiply his hourly wage by the number of hours worked.
For example, if he works $h$ hours, then his total earnings $E$ can be expressed as:
$$ E = 8.25h $$
- Create a table of values
Calculate total earnings for each hour from 0 to 6. The table will have hours worked in one column and total earnings in the next.
| Hours Worked ($h$) | Total Earnings ($E$) |
|---|---|
| 0 | $8.25 \times 0 = 0$ |
| 1 | $8.25 \times 1 = 8.25$ |
| 2 | $8.25 \times 2 = 16.50$ |
| 3 | $8.25 \times 3 = 24.75$ |
| 4 | $8.25 \times 4 = 33.00$ |
| 5 | $8.25 \times 5 = 41.25$ |
| 6 | $8.25 \times 6 = 49.50$ |
- Calculate the rate of change in total earnings
The rate of change can be calculated by determining how much the total earnings increase for each additional hour worked. Since the wage is constant, the rate of change in earnings is equal to his hourly wage:
Rate of Change = $8.25$ (total earnings increase per hour)
- Graph the table values
Plot the points from the table on a graph where the x-axis represents hours worked and the y-axis represents total earnings. Connect these points with a straight line.
Lewis's total earnings after working up to 6 hours are:
- 0 hours: $0
- 1 hour: $8.25
- 2 hours: $16.50
- 3 hours: $24.75
- 4 hours: $33.00
- 5 hours: $41.25
- 6 hours: $49.50
The rate of change in Lewis's total earnings is $8.25 per hour.
More Information
Lewis's earnings indicate a linear relationship, which means for each additional hour he works, he earns an additional $8.25. This can be visualized well in a graph, where the slope represents his hourly wage.
Tips
- Forgetting to convert the earnings calculation for each specific hour worked. Always ensure to multiply the hourly wage by the correct number of hours.
- Not correctly plotting points on the graph. Each point should accurately reflect the corresponding hours and earnings.
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