Exam 1: Linear Equations and Functions

Suppose that the cost C (in dollars) of removing p percent of the particulate pollution from the smokestacks of an industrial plant is given by . Find the domain of this function. Recall that p represents the percent pollution that is removed. ​

Find the market equilibrium point for the following demand and supply functions below, where p is price per unit and q is the number of units produced and sold. ​ Demand: Supply: ​

The percent P of men 65 years of age or older in the labor force can be modeled by , where x is the number of years past 1890 (Source: U.S. Bureau of the Census). Plot this function using a graphing utility. What range of x-values and y-values do you need to use to view this graph for the years 1890 to 1990? ​

Suppose that a company's revenue is a function g of the number of customers C. Suppose also that the amount spent on advertising A affects the number of customers so that is a function f of A. The function is defined, since . Is defined? ​

Choose the correct graph of the line with the given slope and y-intercept.​ ​ Slope: y-intercept: ​

A manufacturer of DVD players has monthly fixed costs of $9,600 and variable costs of $65 unit for one particular model. The company sells this model to dealers for $100 each. Find the manufacturer's profit function where x denotes the number of DVD players produced and sold. ​

The number of millions of short tons of carbon monoxide emissions y in the United States can be described by , where x is the number of years past 1970 (Source: Environmental Protection Agency). Use a graphing utility to plot this function and then use the graph to determine how many short tons of emissions occurred in 1990? ​

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

Find the slope m and y-intercept b of the line whose equation is given below. ​ ​

A woman has $525,000 invested in two rental properties. One yields an annual return of 10% of her investment, and the other returns 12% per year on her investment. Her total annual return from the two investments is $53,000. Let x represent the amount of the 10% investment and y represent the amount of the 12% investment. Find how much is invested in each property by solving the equations for the total amount invested and the return from each property. ​

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 F = 0.551M + 6.686 , where M and F represent the average annual earnings (in thousands of dollars) of males and females, respectively. Choose the correct interpretation of the slope.​ ​

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

A linear revenue function is , where x represents the number of units sold. What is the revenue received from selling one more item if 50 are currently being sold? Round your answer to the nearest cent. ​

A linear revenue function is , where x represents the number of units sold. If 30 units are currently produced, determine the marginal revenue. ​

A manufacturer of DVD players has monthly fixed costs of $8,800 and variable costs of $75 unit for one particular model. The company sells this model to dealers for $100 each. Find the function for total revenue where x denotes the number of DVD players produced and sold. ​

Use the left-to-right elimination method to solve the system. ​ ​ ​

Which of the graphs below represent y as a function of x? ​ (a) ​ (b) ​ ​

Use the left-to-right elimination method to solve the system. ​ ​

Suppose a certain home improvement outlet knows that the monthly demand for framing studs is 1,500 when the price is $1.00 each but that the demand is 2,500 when the price is $0.90 each. Assume the demand function is linear. Choose the correct equation for demand where p denotes price and q denotes quantity. ​

Medication A is given every 4 hours and medication B is given twice each day. The total intake of the two medications is restricted to 45.7 mg per day, for a certain patient. If the ratio of the dosage of A to the dosage of B is 7 to 9, find the dosage for each administration of each medication. ​