Question

A small telephone company charges a $6.00 flat monthly fee, independent of the number of calls a customer makes. The telephone company does charge for the amount of time spent on the phone at the rate of 2.40 per hour. Fractional parts of an hour are billed accordingly. For example, one half hour costs $1.20 fifteen minutes cost $0.60 one minute costs $0.04 and so on Write and graph a function c(t) to model the monthly telephone cost as a function of the time t that the car is parked in the garage

explain and put the answer and


Question 2.A local parking garage charges $6.00 for up to and including 1 hour of parking. Each additional hour, or any part thereof, cost $2.40. Write and graph a function c(t) to model the cost of parking a car as a function of the time t that the car is parked in a garage

Answer 1

1- For the telephone company, the function c(t) to model the monthly telephone cost as a function of the time t that the customer spends on the phone is:
c(t) = 6 + 2.4t
where t is measured in hours and c(t) is measured in dollars.
The flat monthly fee is $6.00 and each hour of phone usage costs $2.40. The function shows that the cost increases linearly with the number of hours spent on the phone.
Graph of the function:

y = 6 + 2.4x

The x-axis represents the time (t) spent on the phone and the y-axis represents the cost. The graph is a straight line with a y-intercept of 6 and a slope of 2.4, indicating that the cost increases by $2.40 for every hour of phone usage.

2- For the parking garage, the function c(t) to model the cost of parking a car as a function of the time t that the car is parked in the garage is:
c(t) = 6 + 2.4*ceiling(t-1)
where t is measured in hours and c(t) is measured in dollars, and ceiling(t-1) is the smallest integer greater than or equal to (t-1)
The first hour of parking costs $6.00 and each additional hour or fraction thereof costs $2.40. The function shows that the cost increases linearly with the number of hours the car is parked in the garage.
Graph of the function:

y = 6 + 2.4*ceiling(x-1)

The x-axis represents the time (t) the car is parked in the garage and the y-axis represents the cost. The graph is a step function with a y-intercept of 6, this means that the first hour of parking is always $6.00, and the height of each step is $2.40, indicating that the cost increases by $2.40 for every additional hour or fraction thereof of parking.

Note: The function c(t) assumes that the time t is measured in hours and that it is a non-negative number.