Concept explainers
Reminder Round all answers to two decimal places unless otherwise indicated.
Marginal Tax Rate Let
a. Explain the meaning of the marginal tax rate in practical terms.
b. The marginal tax rate is normally given as a percentage. Explain in practical terms what a marginal tax rate of
c. You are offered a payment of
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Functions and Change: A Modeling Approach to College Algebra (MindTap Course List)
- Reminder Round all answers to two decimal places unless otherwise indicated. World Copper Production World production of copper, in millions of tons per year, from 1900 to 2000 is given by C=0.51.033t, where t is the time in years since 1900. a.What production level does this model give for the year 2000? b.If this model were extended to 2025, how could you use your knowledge of copper production in 2024 to estimate copper production in 2025?arrow_forwardReminder Round all answer to two decimal places unless otherwise indicated. Real Estate Sales A real estate agency has fixed monthly costs associated with rent, staff salaries, utilities, and supplies. It earns its money by taking a percentage commission on total real estate sales. During the month of July, the agency had total sales of 832,000 and showed a net income after paying fixed costs of 15,704. In August, total sales were 326,000 with a net income of only 532. a. Use a formula to express net income as a linear function of total sales. Be sure to identify what the letters that you use mean. b. Plot the graph of net income and identify the slope and vertical intercept. c. What are the real estate agencys fixed monthly costs? d. What percentage commission does the agency take on the sale of a home? e. Find the horizontal intercept and explain what this number means to the real estate agency.arrow_forwardReminder: Round all answer to two decimal places unless otherwise indicated. 15.Total Cost The total cost C for a manufacturer during a given time period is a function of the number N of items produced during that period. To deter mine a formula for the total cost, we need to know the manufacturers fixed costs covering things such as plant maintenance and insurance, as well as the cost for each unit produced, which is called the variable cost. To find the total cost, we multiply the variable cost by the number of items produced during that period and then add the fixed costs. Suppose that a manufacturer of widgets has fixed costs of 9000 per month and that the variable cost is 15 per widget so it costs 15 to produce 1 widget. a. Use a formula to express the total cost C of this manufacturer in a month as a function of the number of widgets produced in a month. Be sure to state the units you use. b. Express using functional notation the total cost if there are 250 widgets produced in a month, and then calculate that value.arrow_forward
- Reminder Round all answers to two decimal places unless otherwise indicated. Sales Income The following table shows the net monthly income N for a real estate agency as a function of the monthly real estate sales s, both measured in dollars. s=Sales N=Netincome 450,000 4000 500,000 5500 550,000 7000 600,000 8500 a. Make a table showing, for each of the intervals in the tax table above, the average rate of change in N. What pattern do you see? b. Use the average rate of change to estimate the net monthly income for monthly real estate sales of 520,000. In light of your answer to part a, how confident are you that your estimate is an accurate representation of the actual income? c. Would you expect N to have a limiting value? Be sure to explain your reasoning.arrow_forwardReminder Round all answers to two decimal places unless otherwise indicated. Giants Ants and Spiders Many science fiction movies feature animals such as ants, spiders, or apes growing to monstrous sizes and threatening defenseless Earthlings. Of course, they are in the end defeated by the hero and heroine. biologists use power function as a rough guide to relate body weight and cross-sectional area of limbs to length or height. Generally, weight is thought to be proportional to the cube of length, whereas the cross-sectional area of limbs is proportional to the square of length. Suppose an ant, having been exposed radiation is enlarged to 500 times its normal length. Such an event can occur only in Hollywood fantasy. Radiation is utterly incapable of causing such a reaction. a.By how much will its weight be increased? b.By how much will the cross-sectional area of its legs be increased? c.Pressure on a limb is weight divided by cross-sectional area. By how much has the pressure on a leg of the giant ant increased? What do you think is likely to happen to this unfortunate ant? Note: The factor by which pressure increases is given by . FactorofincreaseinweightFactorofincreaseinarea)arrow_forwardReminderRound all answers to two decimal places unless otherwise indicated. Tornadoes In OklahomaThe graph in Figure 1.41 shows the number T=T(d) of tornadoes in Oklahoma Fl/EF1 and stronger reported by the National Climatic Data Center. Round your answers to the nearest whole number. a. When were the most tornadoes reported? How many were reported in that year? b. When were the fewest tornadoes reported? How many were reported in that year? c. What was the average yearly rate of decrease in tornadic activity from 2011 to 2012? d. What was the average yearly rate of increase in tornadic activity from 2009 to 2011? e. What was the average yearly rate of change that is, the average yearly rate of total increase or total decrease in tornadic activity from 2009 to 2012? FIGURE 1.41 Tornadoes in Oklahomaarrow_forward
- Reminder Round all answers to two decimal places unless otherwise indicated. Tax Owed The following table shows the income tax T owed in a certain state as a function of the taxable income I, both measured in dollars. I=Taxableincome T=Taxowed 16,000 870 16,200 888 16,400 906 16,600 924 a. Make a table showing, for each of the intervals in the tax table above, the average rate of change in T. b. Describe the general trend in the average rate of change. What does this mean in practical terms? c. Would you expect T to have a limiting value? Be sure to explain your reasoning.arrow_forwardReminderRound all answers to two decimal places unless otherwise indicated. DensityThe total weight of a rock depends on its size and is proportional to its density. In this context, density is the weight per cubic inch. Let w denote the weight of the rock in pounds, s the size of the rock in cubic inches, and d the density of the rock in pounds per cubic inch. a. What is the total weight of a 3-cubic-inch rock that weighs 2 pounds per cubic inch? b. Write an equation that shows the proportionality relation. What is the constant of proportionality? c. Use the equation you found in part b to find the total weight of a 14-cubic-inch rock with density 0.3 pound per cubic inch.arrow_forwardReminder Round all answer to two decimal places unless otherwise indicated. Lean Body Weight in Males Your lean body weight L is the amount you would weigh if all the fat in your body were to disappear. One text gives the following estimate of lean body weight L in pounds for young adult males: L=98.42+1.08W4.14A, where W is total weight in pounds and A is abdominal circumference in inches. 7 a. Consider a group of young adult males who have the same abdominal circumference. If their weight increases but their abdominal circumference remains the same, how does their lean body weight change? b. Consider a group of young adult males who have the same weight. If their abdominal circumference decreases but their weight stays the same, how does their lean body weight change? c. Suppose a young adult male has a lean body weight of 144 pounds. Over a period of time, he gains 15 pounds in total weight, and his abdominal circumference increases by 2 inches. What is his lean body weight now?arrow_forward
- Reminder Round all answers to two decimal places unless otherwise indicated. Internet Access The following table gives the number I=I(t) in millions, of adult Americans with Internet access in year t. t=Year 2000 2003 2009 I=MillionsofAmericans 113 166 196 a. Find I(2000) and explain what it means. b. Find the average rate of change per year during the period from 2003 to 2009. c. Estimate the value of I(2007). Explain how you got your answer.arrow_forwardReminder Round all answers to two decimal places unless otherwise indicated. Profit The total cost C for a manufacturer during a given time period is a function of the number N of items produced during that period. In this exercise, we measure all monetary values in dollars. To determine a formula for the total cost, we need to know the manufacturers fixed costs covering such things as plant maintenance and insurance as well as the cost for each unit produced, which is called the variable cost. To find the total cost, we multiply the variable cost by the number of items produced during that period and then add the fixed costs. The total revenue R for a manufacturer during a given time period is also a function of the number N of items produced during that period. To determine a formula for the total monthly revenue, we need to know the selling price p per unit of the item, which in general is also a function of N. To find the total revenue, we multiply this selling price by the number of items produced. The profit P for a manufacturer is the total revenue minus the total cost. Suppose that a manufacturer of widgets has a fixed costs of 2000 per month and that the variable cost is 30 per widget. Further, the manufacturer has developed the following table showing the highest price p, in dollars, of a widget at which N widgets can be sold. Number N Price p 200 41.00 250 40.50 300 40.00 350 39.50 a.Use a formula to express the total monthly cost C of this manufacturer as a function of N. b.Use the table to find a linear model of p as a function of N. c.Use your answer to part b to find a formula expressing the total monthly revenue R as function of N. d.Use your answers to part a and part c to find a formula expressing the monthly profit P as a function of N. What type of function is the profit: linear or quadratic? e.Find the two monthly production levels at which the manufacturer just breaks even that is, where the profit is zero.arrow_forwardReminder Round all answers to two decimal places unless otherwise indicated. Arterial Blood Flow Medical evidence shows that a small change in the radius of an artery can indicate a large change in blood flow. For example, if one artery has a radius only 5 larger than another, the blood flow rate is 1.22 times as large. Further information is given in the table below. Increase in radius Times greater blood flow rate 5 1.22 10 1.46 15 1.75 20 2.07 a. Use the average rate of change to estimate how many times greater the blood flow rate is in an artery that has a radius 12 larger than another. b. Explain why if the radius is increased by 12 and then we increase the radius of the new artery by 12 again, the total increase in the radius is 25.44. c. Use parts a and b to answer the following question: How many times greater is the blood flow rate in an artery that 25.44 larger in radius than another? d. Answer the question in part c using the average rate of change.arrow_forward
- Functions and Change: A Modeling Approach to Coll...AlgebraISBN:9781337111348Author:Bruce Crauder, Benny Evans, Alan NoellPublisher:Cengage Learning