Mathematical Modeling Answers

Medical researchers have determined that for exercise to be beneficial, a person’s desirable heart rate, R, in beats per minute, can be approximated by the formulas for women for men, where a represents the person’s age. If the desirable heart rate for a woman is 130 beats per minute, how old is she?

The equation V = -2000t + 20,000 describes the value in dollars of a certain model of car after it is t years old. If a car is worth $14,000, find the age of the car.

A photographer charges a sitting fee of $15, and charges $4 for each 5-in. by 7 in.photograph the customer orders. The linear function can be used to calculate the customer’s cost (c) based on the number of photographs (n) purchased. Determine the cost of 6 photographs.

Solve the problem.Initially a pool contains 250 gallons of water. A hose is placed in the pool, and the water is turned on. The hose adds 5.4 gallons of water per minute. Write a linear model that represents the amount of water, V, in the pool as a function of time, t, in minutes.

Evaluate the function for f(-9).

Solve the problem. The temperature of water in a certain lake on a day in October can be determined by using the model where x is the number of feet down from the surface of the lake and y is the Celsius temperature of the water at that depth. Based on this model, how deep in the lake is the water 9 degrees? (Round to the nearest foot.)

Solve the problem.Williamston Daily is a new daily newspaper. When they first started printing three years ago they had 5600 home delivery subscribers. The number of subscribers increases by 71 every month. Write a linear model that represents the number of subscribers, B, for the number of months, n, the paper has been printed.

Solve the problem. The cost of having a package delivered has a base fee of $9.70. Every pound over 5 lbs cost an additional $0.46 per pound. Write a linear model that represents the cost, C, for the total weight, w, in pounds of the package. Assume w 5 lbs.

Evaluate the function for f(-2).

Solve the problem. A repair company's charge for repairing a certain type of copy machine fits the model where y is the number of dollars charged and x is the number of minutes the repair person is on the job. How many minutes would it take for the cost of repair to reach $130? (Round to the nearest minute.)