Answer:
F(t) = 10 + 5(t)
Step-by-step explanation:
The complete question is as follows;
Anumeha is mowing lawns for a summer job. For each lawn she mows, she charges a $10 starting fee plus an hourly rate. For example, her fee for a 5-hour job is $35. Let f(t) denote Anumeha's fee for a job f (in dollars) based on how many hours (t) were needed to finish it. Write the formula for this function.
Solution
We aim to establish the formula F(t) representing the fee Anumeha charges per job.
Key to formulating this function is understanding the constant charge she applies per job.
We know she earns $35 for mowing for 5 hours.
Therefore, the constant fee can be deduced as follows;
Since it’s a $10 starting fee along with an hourly rate;
35 = 10 + 5(x)
where x refers to the hourly rate
35 = 10 + 5x
5x = 35-10
5x = 25
x = 25/5
x = $5
This indicates that she charges a constant fee of $5 per hour
Thus, we can now write the equation.
F(t) = 10 + 5(t)
where t represents the number of hours spent on each job
x²-9x+12 = (x - (9/2))² - (33/4) For further details, refer to the image below.:)
THE FUNCTION IS CONTINUOUS - True
The table indicates that for every hour indicated, there is a corresponding amount of juice (cups) provided. The graph would represent a linear progression between the hours of 4 and 8 without any discontinuities.
TIME IS THE DEPENDENT VARIABLE - False
Time acts as the independent variable since it remains unaffected by any other factors. Conversely, the number of cups is contingent upon the hours, categorizing it as a dependent variable.
THE SCENARIO IS CHARACTERIZED BY
A LINEAR FUNCTION AS THE RATE OF CHANGE IS CONSTANT - True
The rate of change is a steady 53 cups per hour, indicating a linear function.
AS TIME INCREASES, THERE ARE FEWER CUPS OF JUICE POURED EACH HOUR - False
Since the rate of change is positive, the cups poured each hour will actually increase.
FOR EACH EXTRA HOUR, 53 CUPS OF JUICE ARE POURED - True
The hourly difference in cups poured is consistently 53.
