Final answer:
In a function that calculates the total cost of riding x rides at an amusement park, the coefficient of x represents the cost per ride. For example, in the function f(x) = c * x + b, c is the cost per ride. Using the example of Emma's Extreme Sports, the equation f(x) = 50 + 20x has 20 as the cost per student, analogous to the cost per ride.
Step-by-step explanation:
When considering a function that calculates the total cost, f(x), of riding x rides at an amusement park, the part of the function that represents the cost per ride is the coefficient of x in the function's equation. For instance, if f(x) = c * x + b, where c is a constant representing the cost per ride and b represents any fixed costs (such as an entrance fee or the cost of a ride pass), then c is the value that we're interested in to determine the cost per ride. To apply this to a real-world scenario, let's use Emma's Extreme Sports as an example:
Emma pays hang-gliding instructors a fixed fee of $50 per class, as well as $20 per student. Therefore, the total cost Emma pays, represented by the function f(x), based on the number of students in a class can be expressed as f(x) = 50 + 20x. In this equation, $20 is the cost per student, hence it represents the cost per ride (or per student, in this context).
To further illustrate, if there are x students in a class, Emma's total cost for the class would be $50 (fixed fee per class) plus $20 multiplied by the number of students (x), which gives us the linear equation f(x) = 50 + 20x. The slope of this function, which is 20, directly corresponds to the variable cost per student, which in our amusement park analogy, would be equivalent to the cost per ride.