A. To find the rate of change and initial value, we need to calculate the slope of the line that represents the fees Elliot charges each year. The rate of change is the amount by which the fee increases each year. To find the rate of change, we can use the formula:
Rate of Change = (Change in fee) / (Change in year)
In this case, the change in fee is $1350 - $750 = $600, and the change in year is 2010 - 2000 = 10. So the rate of change is:
Rate of Change = 600 / 10 = 60
Therefore, the rate of change for Elliot's business is $60.
The initial value is the fee that Elliot charged in the first year, which is $750. So the initial value for Elliot's business is $750.
B. To write an equation in slope-intercept form to represent the fees that Elliot charges each year, we can use the equation:
Fee = (Rate of Change) * Year + Initial Value
Plugging in the values we found, the equation becomes:
Fee = 60 * Year + 750
Elliot has been running a lawn care business since 2000. He cuts grass, trims, and weed whacks yards for his customers throughout the season. Each year, he has increased his fee by the same amount. The table shows what Elliot charged each customer for two given years of his business:
Year Lawn Care Fee
2000 $750
2010 $1350
A. What is the rate of change and initial value for Elliot's business? How do you know?
B. Write an equation in slope-intercept form to represent the fees that Elliot charges each year. (
1 answer
1 answer