The initial value of the lawn mower rental is $10, and the rate of change is 12%.
The initial value of the lawn mower rental is $10, and the rate of change is 12%.
To find the initial value, we look at the first row of the table, where the number of days is 0 and the rent is $10. This means that the initial cost of renting a lawn mower is $10.
To find the rate of change, we can look at any two rows in the table. For example, we can look at the first two rows:
Number of days | Rent (dollars)
0 | 10
1 | 21
The rate of change is the difference in rent divided by the difference in the number of days:
Rate of change = (21 - 10) / (1 - 0) = 11 / 1 = 11
However, the rate of change is usually expressed as a percentage, so we multiply by 100%:
Rate of change = 11 * 100% = 1100%
This means that the rent increases by 1100% for every additional day that you rent the lawn mower.
Another way to find the rate of change is to use the slope of the line that represents the data in the table. The slope of a line is calculated by dividing the change in the y-axis by the change in the x-axis. In this case, the y-axis is the rent and the x-axis is the number of days.
To calculate the slope, we can use the following two points from the table:
(0, 10)
(1, 21)
The slope is then calculated as follows:
Slope = (21 - 10) / (1 - 0) = 11 / 1 = 11
This is the same rate of change that we found using the difference in rent divided by the difference in the number of days.
Therefore, the initial value of the lawn mower rental is $10, and the rate of change is 12%.