1-1.1 Mathematical Modeling Answers

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.a.C = 0.19m + 32.99c.C = 0.19mb.C = 32.99(m - 100) + 0.19d.C = 0.19(m - 100) + 32.99

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.) a. 149 c. 48 b. 98 d. 73 Please select the best answer from the choices provided

The value of almost everything you own (assets), such as a car, computer, or house, depreciates (goes down) over time. When an asset’s value decreases by a fixed amount each year, the depreciation is called straight-line depreciation. Suppose your truck has an initial value of $12,400 and depreciates $820 per year. What two variables are involved in this problem? Which variable can best be designated as the dependent variable? As the independent variable?a.Independent variable - amount of depreciation per year;Dependent variable - number of years you own the truck.b.Independent variable - value of the truck;Dependent variable - amount of depreciation per year.c.Independent variable - number of years you own the truck;Dependent variable - value of the truck.d.Independent variable - value of the truck;Dependent variable - number of years you own the truck.

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.a.The number of people infected is decreasing at a steady rate.b.The number of months is increasing quickly.c.The number of people infected is increasing at a very fast rate.d.There is no apparent trend or pattern in the table.

Simple interest on a bank loan can be calculated by multiplying the principal times the interest rate times the time. In the formula , what does I stand for? a. time c. principal b. interest rate d. simple interest Please select the best answer from the choices provided

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. a. $60 b. $35 c. $55 d. $210 Please select the best answer from the choices provided

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.

Evaluate the function for f(4). a. 5 b. 9 c. 11 d. 14 Please select the best answer from the choices provided

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? a. No more than 7 photographs b. No more than 3 photographs c. No more than 8 photographs d. No more than 9 photographs Please select the best answer from the choices provided