intro to maths

Question # 1 The local electric company uses the following method for computing monthly electric bills for one class of customers. A monthly service charge of $5 is assessed for each customer. In addition, the company charges $0.095 per kilowatt hour. If c equals the monthly charge stated in dollars and k equals the number of kilowatt hours used during a month: (a) Determine the function which expresses a customer's monthly charge as a function of the number of kilowatt hours. (b) Use this function to compute the monthly charge for a customer who uses 850 kilowatt hours. Question # 2 Membership Drive A small health club is trying to stimulate new memberships. For a limited time, the normal annual fee of $300 per year will be reduced to $200. As an additional incentive, for each new member in excess of 60, the annual charge for each new member will be further reduced by $2. Determine the function p - f(n), where p equals the membership fee for new members and n equals the number of new members. Question # 3 Salvage Value A major airline purchases a particular type of plane for $75 million. The company estimates that the salvage (resale) value of the plane is estimated well by the function S - f(x) - 72 - 0.0006x where S equals the salvage value (in millions of dollars) and x equals the number of hours of flight time for the plane. (b) What is the salvage value expected to equal after 10,000 hours of flight time? (c) How many hours would the plane have to be flown for the salvage value to equal zero? (d) What interpretation would you give to the y intercept? Why do you think this does not equal 75? Question # 4 Automobile Leasing A car-leasing agency purchases new cars each year for use in the agency. The cars cost $15,000 new. They are used for 3 years, after which they are sold for $4,500. The owner of the agency estimates that the variable costs of operating the cars, exclusive of gasoline, are $0.18 per mile. Cars are leased for a flat fee of $0.33 per mile (gasoline not included). (a) Formulate the total revenue function associated with renting one of the cars a total of x miles over a 3-year period. (b) Formulate the total cost function associated with renting a car for a total of x miles over 3 years. (c) Formulate the profit function. (d) What is profit if a car is leased for 60,000 miles over a 3-year period? (e) What mileage is required in order to earn zero profit for 3 years? Question # 5 A police department believes that arrest rates R are a function of the number of plainclothes officers n assigned. The arrest rate is defined as the percentage of cases in which arrests have been made. It is believed that the relationship is linear and that each additional officer assigned to the plainclothes detail results in an increase in the arrest rate of 1.20 percent. If the current plainclothes force consists of 16 officers and the arrest rate is 36 percent: (a) Define the function R = f(n). (b) Interpret the meaning of the R intercept. (c) Determine the restricted domain and range for the function. (d) Sketch the function