Describe a real life situation that could be modeled by a function.
A real life situation is:
A family decides that they want to get the carpet done in their house. They already have all the necessary material to do the work but they do not know how. They need to hire someone to do the work for them. They find a company that charges $35 an hour to install the carpet. It will take 12 hours to get the carpet done in the house. The domain is the (x)$35 that the company charges for labor multiplied by the range which is the (y)12 hours it will take to get done. This means that the output is the total amount that the family will be paying for the labor for the work to be done. I believe that this is a function because there is only one possible output that can come out of this equation.
Yes, you are correct. The situation can be modeled by a function. Let's denote the number of hours of work as x and the corresponding cost of labor as y. The relationship between x and y can be described by the function f(x) = 35x, where f(x) represents the total cost of labor. As x increases by 1 hour, the cost of labor (y) will increase by $35. In this case, since it will take 12 hours to complete the carpet installation, the total cost of labor will be f(12) = 35 * 12 = $420. Therefore, the function models the relationship between the number of hours and the cost of labor in this real-life situation.
Yes, you are correct. The situation you described can be modeled by a function. Let's break it down step by step to understand how to model it mathematically.
In this situation, we have the following variables:
x: The cost per hour charged by the company ($35 in this case)
y: The number of hours required to install the carpet (12 hours)
The total amount the family will pay for the labor can be calculated by multiplying the cost per hour by the number of hours:
Total cost = x * y
Substituting the values, we get:
Total cost = $35 * 12
Simplifying the expression, we find that the total cost is $420.
So, the function that models this real-life situation is:
f(x) = 35x
where f(x) represents the total cost in dollars and x represents the number of hours.
This is indeed a function, as each input (number of hours) will give a unique output (total cost). In this example, the total cost varies linearly with the number of hours, with a rate of $35 per hour.