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What Formulas Mean In Exercises S-25 through S-33, you are asked to relate functional notation to practical explanations of what certain functions mean.
Time to Pay Off a Loan The function
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Functions and Change: A Modeling Approach to College Algebra (MindTap Course List)
- What Formulas Mean In Exercises S-25 through S-33, you are asked to relate functional notation to practical explanations of what certain functions mean. Grocery Bill If c(p,s,h) is the cost of buying p bags of potato chips, ssodas, and h hot dogs, use functional notation to express the cost of buying 2 bags of potato chips, 3 sodas, and 5 hot dogs.arrow_forwardWhat Formulas Mean In Exercises S-25 through S-33, you are asked to relate functional notation to practical explanations of what certain functions mean. Dow Jones Industrial Average The function D(t) gives the Dow Jones Industrial Average t minutes after noon today. Explain in practical terms the meaning of D(120).arrow_forwardGrowth in Length of Haddock D.S. Raitt found that the length L of haddock in centimeters as a function of the age t in years is given approximately by the formula L=5342.820.82t a. Calculate L(4) and explain what it means. b. Compare the average yearly rate of growth in length from age 5 to age 10 years with the average yearly rate of growth from age 15 to age 20 years. Explain in practical terms what this tells you about the way haddock grow. c. What is the longest haddock you would expect to find anywhere?arrow_forward
- Growth in Weight and Height Between the ages of 7 and 11 years, the weight w, in pounds, of a certain girl is given by the formula w=8t. Here t represents her age in years. a. Use a formula to express the age t of the girl as a function of her weight w. b. At what age does she attain a weight of 68 pounds? c. The height h, in inches, of this girl during the same period is given by the formula h=1.8t+40. i. Use you answer to part b to determine how tall she is when she weighs 68 pounds. ii. Use a formula to express the height h of the girl as a function of her weight w. iii. Answer the question in part i again, this time using your answer to part ii.arrow_forwardLater Public High School Enrollment Here is a model for the number of students enrolled in U.S. public high schools as a function of time since 2000. N=0.033t2+0.46t+13.37 In this formula, N is the enrollment in millions of students, t is the time in years since 2000, and the model is applicable from 2000 to 2010. a. Calculate N(10) and explain in practical terms what it means. b. In what year was the enrollment the largest? c. Find the average yearly rate of change in enrollment from 2004 to 2010. Is the result misleading, considering your answer to part b?arrow_forwardResale Value: The resale value V, in dollars, of a certain car is a function of the number of year t since the year 2012. In the year 2012, the resale ale is 18,000 and each year thereafter the resale value decreases by 1700. a. What is the resale value in the year 2013? b. Find a formula for V as a function of t. c. Make a graph of V versus t covering the first 4 years since the year 2012. d. Use functional notation to express the resale value in the year 2015, and then calculate that value.arrow_forward
- Planet Growth The amount of growth of plants in an ungrazed pasture is a function of the amount of plant biomass already present and the amount of rainfall. For a pasture in the arid zone of Australia the formula Y=55.120.01535N0.00056N2+3.946R gives an approximation of the growth. Here R is the amount of rainfall, in millimeters, over a 3 month period; N is the plant biomass, in kilograms per hectare, at the beginning of that period; and Y is the growth, in kilograms per hectare, of the biomass over that period. For comparison, 100 millimeters is about 3.9 inches, and 100 kilograms per hectare is about 89 pounds per acre. For this exercise, assume that the amount of plant biomass initially present is 400 kilograms per hectare, so N=400. a. Find a formula for the growth Y as a function of the amount R of rainfall. b. Make a graph of Y versus r. Include values of R from 40 to 160 millimeters. c. What happens to Y as R increases? Explain your answer in practical terms. d. How much growth will there be over a 3 month period if initially there are 400 kilograms per hectare of plant biomass and the amount of rainfall is 100 millimeters?arrow_forwardMcDonalds The formula M(t)=1.19t+13.22 gives the approximate total revenue for McDonalds, in billions of dollars, t years after 2000. The formula applies to the years 2000 through 2013. a. Explain in practical terms the meaning of M(5). b. Use functional notation to express the total revenue for 2010. c. Calculate the total revenue in 2010.arrow_forwardInflation Assuming that the annual rate of inflation averages 4 over the next 10 years, the approximate costs C of goods or services during any year in that decade can be modeled by Ct=P1.04t, where t is the time in years and P is the present cost. The price of an oil change for your car is presently $29.88. Estimate the price 10 years from now.arrow_forward
- Growth of North Sea Sole The length of North Sea sole, a species of fish, can be determined using the von Bertalanffy model by the formula L=14.819.1060.631t. Here t is age, in years, and L is length, in inches. a. Make a graph L versus t. Include values of t from 1 to 10 years. b. Use functional notation to express the length of a 4-year-old sole, and that calculate that value. c. At what age will a sole be 10 inches long? d. What is the limiting length for a North Sea sole?arrow_forwardTax Owed According to the Oklahoma Income Tax Table for 2010, the income tax owed by an Oklahoma resident who is married and filing jointly with a taxable income above 100, 000 is 5070 plus 5.5 of the taxable income over 100, 000. a. Use a formula to express the tax owed as a function of the taxable income, assuming that the taxable income is above 100, 000. Be sure to explain the meaning of the letters you choose and the units. b. What is the tax on a taxable income of 108, 650? Round your answer to the nearest dollar. c. For what taxable income would the tax be 5686?arrow_forwardTitanic At 2:00 p.m. on April 11, 1912, the Titanic left Cobh, Ireland, on her voyage to New York City. At 11:40 p.m. on April 14, the Titanic struck an iceberg and sank, having covered only about 2100 miles of the approximately 3400-mile trip. (a) What was the total duration of the voyage in hours? (b) What was the average speed in miles per hour? (c) Write a function relating the distance of the Titanic from New York City and the number of hours traveled. Find the domain and range of the function. (d) Graph the function in part (c).arrow_forward
- Functions and Change: A Modeling Approach to Coll...AlgebraISBN:9781337111348Author:Bruce Crauder, Benny Evans, Alan NoellPublisher:Cengage LearningTrigonometry (MindTap Course List)TrigonometryISBN:9781337278461Author:Ron LarsonPublisher:Cengage Learning