In order to calculate the total cost of renting a car, we need to determine two main costs: the cost related to the number of days the car was rented, and the cost related to the number of miles the car was driven.
(a) Let's first calculate the total for renting the car for 5 days and driving it for 200 miles.
The rental car agency charges $25.00 per day. For 5 days, this will be: $25 * 5 = $125.00
The agency also charges $0.28 per mile. For 200 miles, this will be: $0.28 * 200 = $56.00
So, the total charge would be the sum of the above two costs: $125.00 (for days) + $56.00 (for miles) = $181.00
Hence, the rental charge if you rent a car for 5 days and drive 200 miles would be $181.00 (rounded to the nearest cent).
(b) Now, let's express the cost of renting a car as a function of the number of days (d) and the number of miles (m).
The company charges a fixed daily rate and a fixed rate per mile. So, we can create a function to calculate the total cost depending on the number of days and miles. We are following the same method as before, but this time we generalize it for any number of days and miles.
The cost function C(d, m) can be defined as follows:
C(d, m) = (daily_rate * d) + (mile_rate * m)
Where the daily_rate is $25.00 and the mile_rate is $0.28.
This is a function that takes the number of days and miles, calculates the respective costs, and returns the total cost. It provides a formula to easily determine the total cost of renting a car for any number of days and miles.
Note: Both the daily and mileage rate should be in the same currency for the function to provide a valid result.