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Question

To charter a fishing boat for 3 hours, the captain charges a base fee of $45.00 plus $15.00 per person.

Using variables, construct a function that models the total cost of a 3-hour charter in terms of the number of people. In your function, define any variables you use.

In terms of the situation modeled by this function, what is the correct interpretation of the initial value and the rate of change?

Answer 1

C(p) = 45 + 15p where total cost and p = number of persons

rate of change is the slope = $15 per person

initial value is $45, the Cost with zero persons. although no one would rent the fishing boat to get zero people on board. Just as they couldn't rent it for negative numbers of people, such as -6 people with a net "cost" of negative $45, as if the captain would pay you to rent the boat. so the "initial value" might more appropriately be $60 for one person. The domain is from p = 1 to some finite number, the max passenger load, before the ship sinks or they run out of life preservers.