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 man is 135 beats per minute, how old is he?

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. How many photographs can be purchased if you cannot spend more than $50.00?

Evaluate the function for f(4).

Solve the problem. When going more than 38 miles per hour, the gas mileage of a certain car fits the model where x is the speed of the car in miles per hour and y is the miles per gallon of gasoline. Based on this model, at what speed will the car average 15 miles per gallon? (Round to nearest whole number.)

The formula is used when calculating:

As part of a community service project at your high school, you are organizing a fund-raiser at the neighborhood movie theater. Money raised will benefit a summer camp for children with special needs. The admission charge is $10.00 per person, $5.50 of which is used to pay the movie theater’s rental fee. The remainder is donated to the summer camp fund.There are two variables involved in this problem. Which variable can best be designated as the dependent variable? As the independent variable?a.Independent variable - number of persons attending (or number of tickets sold);Dependent variable - the amount donatedb.Independent variable - the amount donated;Dependent variable - number of persons attending (or number of tickets sold)c.Independent variable - number of persons attending (or number of tickets sold);Dependent variable - the amount of the admission per persond.Independent variable - number of persons attending (or number of tickets sold);Dependent variable - the amount paid towards the movie theater’s rental fee.

Rich’s weekly salary is based on the number of pairs of shoes he sells. He is paid a base salary of $25, plus $5 for every pair of shoes he sells. The relationship between his pay (p) and pairs of shoes (s) sold can be represented by the linear equation . Determine Rich’s pay for a week in which he sold 7 pairs of shoes.

Solve the problem. Joe is going to travel to Dallas. He lives 360 miles away and can average 60 miles per hour. Write a linear model that represents Joe's distance from Dallas, d(t), traveled as a function of time, t, in hours.

The pressure, p, of water (in pounds per square foot) at a depth of d feet below the surface is given by the formula If a diver is 100 feet below the surface, what is the pressure of the water on the diver?

The following table gives the number of people infected by the flu over a given number of months. Number of Months012345Number of People Infected15133378180Describe any trends or patterns that you observe.

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. What would the desirable heart rate be for a 46 year old woman?

Solve the problem.Bill bought a new cellular phone. His monthly bill will be $32.99 each month which includes 100 minutes of use. Additional minutes will cost $0.19 per minute. Write a linear model that represents the amount of the bill, C, based on the total number of minutes, m, the phone is used in a month. Assume m 100 minutes.