Answer :
To determine the formula that best models Kyle’s hourly rate each year, we need to consider a few factors such as whether his hourly rate increased at a constant rate, exponentially, or in some other pattern over the five years.
Assuming Kyle’s hourly rate increased linearly, which is a common scenario, we can use the formula for a line, which is ( y = mx + b ), where ( y ) represents the hourly rate, ( x ) represents the number of years, ( m ) is the rate of increase per year, and ( b ) is the starting hourly rate.
Given that Kyle made $14.62 in his fifth year, we can plug in the values we know: ( y = 14.62 ) when ( x = 5 ).
However, without additional information about his starting hourly rate or the rate of increase, we cannot determine the exact values for ( m ) and ( b ). If you have more data points from other years, we could use them to calculate the rate of increase and the starting hourly rate, thus defining the formula more precisely.
If the increase is not linear, then other models such as exponential might be more appropriate, which can be represented by ( y = a \cdot b^x ), where ( a ) is the starting amount and ( b ) is the growth factor.
To find the formula that models Kyle's hourly rate each year, we can use a linear equation since his earnings are increasing by a constant amount each year. The formula for a linear equation is:
Hourly rate = m * year + b
where:
- m is the rate of increase per year (slope)
- b is the initial hourly rate (y-intercept)
Given that Kyle made $14.62 in his fifth year, we can substitute the values into the equation:
14.62 = 5m + b
To find the best formula, we need another data point. If you have the earnings from another year, we can use it to solve for m and b to get the formula that models Kyle's hourly rate each year.
Hourly rate = m * year + b
where:
- m is the rate of increase per year (slope)
- b is the initial hourly rate (y-intercept)
Given that Kyle made $14.62 in his fifth year, we can substitute the values into the equation:
14.62 = 5m + b
To find the best formula, we need another data point. If you have the earnings from another year, we can use it to solve for m and b to get the formula that models Kyle's hourly rate each year.
