Final answer:
A linear cost function for a ski resort charging a $40 rental fee plus $6.25 per hour is C = 40 + 6.25h, where 'h' is the number of hours of rental and 'C' is the total cost.
Step-by-step explanation:
To write a linear cost function for the scenario where a ski resort charges a snowboard rental fee of $40 plus $6.25 per hour, you need to identify the fixed cost and the variable cost per hour. The fixed cost, which does not change regardless of the number of hours of rental, is $40. The variable cost, which depends on the number of hours the snowboard is rented, is $6.25 per hour.
The total cost (C) to rent a snowboard for a given number of hours (h) can be represented by the linear equation C = 40 + 6.25h. Here, $40 is the y-intercept, representing the initial rental fee, and $6.25 is the slope of the equation, representing the rate at which the total cost increases for each additional hour of rental.
The independent variable in this situation is the number of hours (h) the snowboard is rented for, and the dependent variable is the total cost (C) for the rental.