Concept explainers
Reminder Round all answers to two decimal places unless otherwise indicated.
Gross Tonnage The gross tonnage
In this exercise, round your answers to the nearest whole number.
a. Find the gross tonnage of a ship with a volume of
b. Use the crossing-graphs method to find the volume of a ship with a gross tonnage of
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Chapter 4 Solutions
Functions and Change: A Modeling Approach to College Algebra (MindTap Course List)
- Reminder Round all answers to two decimal places unless otherwise indicated. The pH Scale Acidity of a solution is determined by the concentration H of hydrogen ions in the solution measured in moles per liter of solution. Chemists use the negative of the logarithm of the concentration of hydrogen ions to define the pH scale: pH=logH Lower pH values indicate a more acidic solution. a.Normal rain has a pH value of 5.6. Rain in the eastern United States often has a pH level of 3.8. How much more acidic is this than normal rain? b.If the pH of water in lake falls below a value of 5, fish often fail to reproduce. How much more acidic is this than normal water with a pH of 5.6?arrow_forwardReminder Round all answers to two decimal places unless otherwise indicated. Logistic Model A population grows according to the logistic model. The r value is 0.02 and the environmental carrying capacity is 2500. Write the logistic equation satisfied by the population if N(0)=100.arrow_forwardReminder Round all answers to two decimal places unless otherwise indicated. Growth Rate An animal grows according to the formula L=0.6log(2+5T). Here L is the length in feet and T is the age in years. a.Draw a graph of length versus age. Include ages up to 20 years. b.Explain in practical terms what L(15) means, and then calculate that value. c.How old is the animal when it is 1foot long? d.Explain in practical terms what the concavity of the graph means. e.Use the formula to express the age as a function of the length.arrow_forward
- Reminder Round all answers to two decimal places unless otherwise indicated. Growth of Bacteria The organism E. coli is a common bacterium. Under certain conditions, it undergoes cell division approximately each 20minutes. During cell division, each cell divides into two cells. a.Explain why the number of E. coli cells present is an exponential function of time. b.What is the hourly growth factor for E. coli? c.Express the population N of E. coli as an exponential function of time t measured in hours. Use N0 to denote the initial population. d.How long will it take a population of E. coli to triple in size?arrow_forwardReminder Round all answers to two decimal places unless otherwise indicated. Dispersion Model Animal populations move about and disperse. A number of models for this dispersion have been proposed, and many of them involve the logarithm. For example, in 1965, O.H.Paris released a large number of pill bugs and after 12 hours recorded the number n of individuals that could be found within r meters from the point of release. He reported that the most satisfactory model for this dispersion was n=0.772+0.297logr+6.991r. a.Make a graph of n versus r for the circle around the release point with the radius 15 meters. b.How many pill bugs were to be found within 2 meters from the release point? c.How far from the release point would you expect to find only a single individual?arrow_forwardReminder Round all answers to two decimal places unless otherwise indicated. Doubling Time If an investment earns an APR of r, as a decimal, compounded annually, then the time D, in years, required for the investment to double in value is given by D=log2log(1+r). a.Find the doubling time for an investment subject to an APR of 5 if interest is compounded annually. b.Plot the graph of the doubling time D versus the interest rate r, as a decimal. Use a horizontal span of 0 to 0.1. c.Does a small change in the interest rate have a greater effect on the doubling time if interest rates are low or if they are high?arrow_forward
- Reminder Round all answers to two decimal places unless otherwise indicated. Minimum Monthly PaymentSuppose you have a balance of B dollars on credit card.You choose to stop charging and pay off the card, making only minimum monthly payments.If your card charges an APR of r, as a decimal, and requires a minimum monthly payment of 5 of the balance, then the time T, in months, required to reduce your balance to 100 is given by T=2logBlog(0.95(1+r/12)). Suppose your current balance is 8000. a.How long will it take to reduce your balance to 100 if the APR for your card is 25? Report your answer to the nearest whole month. b.Plot the graph of T versus r. Use a horizontal span of 0 to 0.3. c.Does a larger APR mean a longer or a shorter time to reduce the balance to 100?arrow_forwardReminder Round all answers to two decimal places unless otherwise indicated. Theater Production Data from the Statistical Abstract of the United States show that in 1995, there were 56.61 thousand performances in the United States by nonprofit professional theaters. From 1995 through 2007, this number increased on average by about 10 each year. a.Let P denote the number of performances, in thousands, and let t denote the time in years since 1995. Make an exponential model for P versus t. b.How many performances by non-profit professionals theaters does your model give for 2007? The actual number was 197 thousand.arrow_forwardReminder Round all answers to two decimal places unless otherwise indicated. Whispers A whisper in a quiet library is about 30decibels. What decibel level would be recorded by a table of 10 library patrons, each whispering at 30decibels?arrow_forward
- Reminder Round all answers to two decimal places unless otherwise indicated. An Investment You have invested money in a savings account that pays a fixed monthly interest on the account balance. The following table shows the account balance over the first 5 months. Time, in months Saving balance 0 1750.00 1 1771.00 2 1792.25 3 1813.76 4 1835.52 5 1857.55 a. How much money was originally invested? b. Show that the data are exponential and find an exponential model for the account balance. c. What is the monthly interest rate? d. What is the yearly interest rate? e. Suppose that you made this investment on the occasion of the birth of your daughter. Your plan is to leave the money in the account until she starts college at age 18. How large a college fund will she have? f. How long does it take your money to double in value? How much longer does it take it to double in value again?arrow_forwardReminder Round all answers to two decimal places unless otherwise indicated. Magnitude and EnergyThe magnitude M of an earthquake is related to the energy E that it releases.The formula is M=logE+7.51.5. Here the unit of energy is the terajoule, which is one trillion joules. One joule is approximately the energy expended in lifting 3/4 of a pound one foot. One terajoule is approximately the energy produced by burning one million cubic feet of natural gas. a.What is the magnitude of a 10-terajoule earthquake? Round your answer to one decimal place. b.On September 24, 2013, a quake of magnitude 7.7 struck Pakistan. How much energy was released by that quake? c.The atomic bomb dropped on Hiroshima released about 60terajoules of energy. How many such bombs would be needed to produce the energy released by the Pakistan quake from part b? Round your answer to the nearest whole number.arrow_forwardReminder Round all answers to two decimal places unless otherwise indicated. Gray Wolves in Idaho The report cited in Example 4.6 tells us that in 2009, there were 870 gray wolves in Idaho, but that the population declined by 19 that year. For purposes of this problem, we assume that this 19 annual rate of decrease continues. a. Find an exponential model that gives the wolf population W as function of the time t in years since 2009. b. It is expected that the wolf population cannot recover if there are fewer than 20 individuals. How long must this rate of decline continue for the wolf population to reach 20?arrow_forward
- Functions and Change: A Modeling Approach to Coll...AlgebraISBN:9781337111348Author:Bruce Crauder, Benny Evans, Alan NoellPublisher:Cengage Learning