Reminder Round all answers to decimal places unless otherwise indicated.
Health Plan The managers of an employee health plan for a firm have studied the balance
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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. Sales Growth A study of the sales s, in thousands of dollars, of a product as a function of time t, in years, yields the equation of change dsdt=0.3s(4s). This is valid for s less than 5. a.What level of sales will be attained in the long run? b.What is the largest rate of growth in sales?arrow_forwardReminder Round all answers to two decimal places unless otherwise indicated. Note Some of the formulas below use the special number e, which was presented in the Prologue. The height of the winning pole vault in the early years of the modern Olympic Games can be modeled as a function of time by the formula H=0.05t+3.3 Here t is the number of years since 1900, and H is the winning height in meters. One meter is 39.37 inches. a. Calculate H(4) and explain in practical terms what your answer means. b. By how much did the height of the winning pole vault increase from 1900 to 1904? From 1904 to 1908?arrow_forwardReminder Round all answer to two decimal places unless otherwise indicated. Hair Growth When you are 18 years old you have a hair that is 14 centimeters long, and your hair grows about 12 centimeters each year. Let H(t) be the length, in centimeters, of that hair t years after age 18. a. Find a formula that gives H as a linear function of t. b. How long will it take for the hair to reach a length of 90 centimeters?arrow_forward
- Reminder Round all answers to two decimal places unless otherwise indicated. Kleibers law states that for the vast majority of animals, the metabolic rate M is a power function of the weight W, and the power is k=34. a.The Eastern gray squirrel weighs about 1 pound. How does the squirrels metabolic rate compare with that of a 200 -pound man? b.How does a 200- pound mans metabolic rate compare with that of a 130- pound woman? c.Based on your answer to part b, would overeating the same amount for each be more likely to lead to weight gain for the man or for the woman?arrow_forwardReminder Round all answers to two decimal places unless otherwise indicated. Account Growth The table below shows the balance B in a savings account, in dollars, in terms of time t, measured as the number of years since the initial deposit was made. Time t Balance B 0 125.00 1 131.25 2 137.81 3 144.70 4 151.94 a. Was the yearly interest rate constant over the first 4 years? If so, explain why and find that rate. If not, explain why not. Round the ratios to two decimal places. b. Estimate B(2.75) and explain in practical terms what your answer means. Assume that interest is compounded and deposited continuously.arrow_forwardReminder: Round all answer to two decimal places unless otherwise indicated. a. How much does it cost to prepare and mail a 3-page letter if your secretary spends 2 hours on typing and corrections? b. Use a formula to express the cost of preparing and mailing a letter as a function of the number of pages in the letter and the time it takes your secretary to type it. Identify the function and each of the variables you use, and state the units. c. Use the function you made in part b to find the cost of preparing and mailing a 2-page letter that it takes your secretary 25 minutes to type. Note: 25 minutes is 25/60 hour.arrow_forward
- ReminderRound all answers to two decimal places unless otherwise indicated. Minimum WageOn July 24, 2008, the federal minimum wage was 6.55perhour. On July 24, 2009, this wage was raised to 7.25perhour. If W(t) denotes the minimum wage, in dollars per hour, as function of time, in years, use the given information to estimate dWdt in 2009.arrow_forwardReminder 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 answers to two decimal places unless otherwise indicated. t is measured in thousands of years, and C=C(t) is the amount, in grams, of carbon-14 remaining. Carbon-14 unstable radioactive t=Thousandofyears C=Gramsremaining 0 5 5 2.73 10 1.49 15 0.81 20 0.44 a. What is the average yearly rate of change of carbon-14 during the first 5000 years? b. How many grams of carbon-14 would you expect to find remaining after 1236 years? c. What would you expect to be the limiting value of C?arrow_forward
- Reminder Round all answers to two decimal places unless otherwise indicated. WendysAccording to a report in The Wall Street Journal, Wendys revenue fell 3.2 to 489.5million in the second quarter of 2015. That represents a quarterly decay rate, as a decimal of e0.0325. Let R(t) denote Wendys revenue, in millions of dollars, t quarters after the second quarter of 2015. Suppose that revenue continues to fall at this same rate. a.Write the equation of change for Wendys revenue. b.Find a formula that gives Wendys revenue t quarters after the second quarter of 2015.arrow_forwardReminder Round all answers to two decimal places unless otherwise indicated. A wedding Reception You rent a wedding venue for a cost of 3200. The cost includes a catered lunch for 50 guests. For each addition guest, though, the catered lunch costs 31. a. What is the cost of the venue and lunch if you invite 100 guests. b. Find a formula showing the cost of the venue and the lunch as a function of n, the number of guests. Assume that n is at least 50. c. The amount you have budgeted for the venue and catered lunch is 5500. How many guests can you invite.arrow_forwardReminder Round all answers to two decimal places unless otherwise indicated. Getting Celsius Fro Fahrenheit Water freezes at 0 degrees Celsius, which is the same as 32 degrees Fahrenheit. Also, water boils at 100 degrees Celsius, which is the same as 212 degrees Fahrenheit. a. Use the freezing and boiling points of water to find a formula expressing Celsius temperature C as a linear function of the Fahrenheit temperature F b. What is the slope of the function you found in part a? Explain its meaning in practical terms. c. In Example 3.5, we showed that F=1.8C+32. Solve this equation for C and compare the answer with that obtained in part a.arrow_forward
- Functions and Change: A Modeling Approach to Coll...AlgebraISBN:9781337111348Author:Bruce Crauder, Benny Evans, Alan NoellPublisher:Cengage Learning