Exercises with Answers

Section 3.3 Equations of Lines 285so let number sold n be the independentvariable and profit P , in $, be the dependentvariable.a) On a sheet of graph paper, make agraph to model this situation, goingas far as n = 15.b) Use the graph to predict the profit ifn = 10 DVD’s are sold.c) The graphical model is limited to predictingfor values of n on your graph.Any larger value of n necessitates alarger graph, or a different kind ofmodel. To begin finding an algebraicmodel, identify the P -intercept of thegraph.d) What is the slope of the line in yougraphical model?e) Find a slope-intercept form of a linearfunction that models Blue CharlesCo.’s sales.f) Write the function using function notation.g) Explain why this model does not havethe same limitation as the graphicalmodel.h) Find P (100), P (1000), and P (10000).i) In complete sentences, explain whatthe values of P (100), P (1000), andP (10000) mean in the context of theproblem.15. Enrique had $1, 000 saved when hebegan to put away an additional $25 eachmonth.a) Let t represent time, in months, andS represent Enrique’s savings, in $.Identify which should be the independentand dependent variables.b) To begin finding a linear function tomodel this situation, identify the S-intercept and slope.c) Find a slope-intercept form of a linearfunction to model Enrique’s savingsover time.d) Write the linear function in functionnotation.e) Use the function model to predicthow much will be in his savings inone year.f) Use the function model to predict whenwill he have $2000 saved.g) Graph the function on a coordinatesystem.h) At the same time, Anne-Marie alsobegins to save $25 per month, but shebegins with $1200 already in her savings.Make a graphical model of hersituation and place it on the same coordinatesystem as the graphical modelfor Enrique’s savings. Label it appropriately.i) How do the lines compare to eachother? Say something about their slopes.j) Find a slope-intercept form of a linearfunction that models Anne-Marie’ssavings. Use the same variables asyou did for Enrique’s model.k) Write the function using function notation.l) Prove that the graphs of the two functionsare parallel lines.m) For Anne-Marie, looking at the graphs,do you think it will take her moretime or less time than Enrique to saveup $2000?.Version: Fall 2007