How Can A Model Be Used To Answer Questions About Its Graph?

These problems each require you to utilize a graph to answer parts of the question. The difficulty is often gauging what the window should be. If you understand what the variables represent, your task is easier. For instance, in the first problem you know that the input has to do with years since 1995 and the outputs are percentages. This gives a lot of insight to an appropriate window.

Problem 1 The function \displaystyle P=5.8t+7.13 gives the percent of households with Internet access as a function of t, the number of years after 1995.

a. What are the values of t that correspond to the years 1996 and 2014?

b. P = f(10) gives the value of P for what year? What is f(10)?

c. What xmin and xmax should be used to set the viewing window so that t represents 1995-2015.

Where is the error in this solution?

Problem 2 The total cost of prizes and expenses of state lotteries is given by \displaystyle P=35{{t}^{2}}+740t+1207 million dollars, with t equal to the number of years after 1980.

a. What are the values of t that correspond to the years 1988, 2000, and 2012?

b. P = f(14) gives the value for P for what year? What is f(14)?

c. What xmin and xmax should be used to set a viewing window so that t represents 1980-2007?

Solution for Problem 1.2.36 from text

Good work by these students! They actually did more than what the problem asked for.

Problem 3 A model that relates the median annual salary (in thousands of dollars) of females, F, and males, M, in the United States is given by \displaystyle F=0.78M-1.05.

a. Use a graphing utility to graph this function on a viewing window [0,100] by [0,80].

b. Use the graphing utility to find the median female salary that corresponds to a male salary of $63,000.

Many errors can be avoided by paying careful attention to the units on the variables (years since 1900, millions of women, thousands of dollars)! For instance, on the last problem a male salary of $63,000 corresponds to M = 63, NOT M = 63,000.