Exam 2: Linear Equations and Functions

According to the U.S. Bureau of the Census, the relation between the average annual earnings of males and females with various levels of educational attainment can be modeled by the function where M and F represent the average annual earnings (in thousands of dollars) of males and females, respectively. When the average annual earnings for males reach $45,000, what does the equation predict for the average annual earnings for females? Round your answer to the nearest dollar. ​

If t represents the number of hours after 9:30 A.M. on Tuesday, October 5, 2004, then the graph defines the Dow Jones Industrial Average D as a function of time t. If we represent this function by use the graph to find f(6.5). ​ ​ Source: Bloomberg Financial Markets, The New York Times, October 6, 2004. Copyright © 2004 The New York Times Co. Reprinted by permission. ​

Suppose the cost C of removing p percent of the particulate pollution from the exhaust gases at an industrial site is given by . Because p is the percent particulate pollution, we know . Use the restriction on p and experiment with a C-range to obtain an accurate graph of the equation. Determine the p-intercept and explain its meaning. ​

A linear revenue function is , where x represents the number of units sold. What is the revenue received from selling one more item if 75 are currently being sold? Round your answer to the nearest cent. ​

Let and . Does for all values of x and h? ​

Find the intercepts of the following function. ​ ​

For and , find . ​

If , find . ​

Write the equation of the line passing through the given pair of points. ​ (3,9) and (11,1) ​

Use the x-intercept method to find the solution to this equation. ​ ​

Each ounce of substance A supplies 4% of the nutrition a patient needs. Substance B supplies 29% of the required nutrition per ounce, and substance C supplies 14% of the required nutrition per ounce. If digestive restrictions require that substances A and C be given in equal amounts, and the amount of substance B be one-fifth of either of these other amounts, find the number of ounces of each substance that should be in the meal to provide 100% of the required nutrition. ​

Suppose a computer manufacturer has the total cost function and the total revenue function , where x represents the number of computers produced and sold. What is the profit on 351 items? ​

What is the rate of change of the function whose graph is a line passing through and ? ​

Solve the system by elimination, or by any convenient method. ​ ​

Suppose that in a certain market, the demand function for a product is given by and the supply function is given by , where p is the price per unit in dollars and q is the quantity produced. If the government levies a tax of $9 per item on the supplier, who passes the tax on to the consumer as a price increase, find the equilibrium price and quantity after the tax is levied. Round q to the nearest whole number and round p to one decimal place. ​

Solve the inequality. ​ ​

Use a graphing utility with the standard viewing window and to graph the function. Choose the correct graph below. ​ ​

Solve the inequality and choose the graph of the solution. ​ ​

Suppose that the total cost function for a radio is linear, that the marginal cost is $27, and that the total cost for 50 radios is $5,250. Write the equation of this cost function . ​

The equation in this problem leads to a linear equation. Solve for x. Because the solution to the linear equation may not be a solution to the original equation, be sure to check the solution in the original equation. ​ ​