Concept explainers
Reminder Round all answers to two decimal places unless otherwise indicated.
Stand Density Forest managers are interested in measures of hot crowed a given forest is. One measurement used is the stand density index, or SDI. It can be related to the number
a. A stand has
b. What is the effect on the stand density index of increasing the number of trees per acre by a factor of
c. What is the relationship between the stand-density index and the number of trees per acre if the diameter of a tree of average size is
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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. 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. Note Some of the formulas below use the special number e, which was presented in the Prologue. A Population of Deer When a breeding group of animals is introduced into a restricted area such as a wildlife reserve, the population can be expected to grow rapidly at first, but to level out when the population grows to near the maximum that the environment can support. Such growth is known as logistic population growth, and ecologists sometimes use a formula to describe it. The number N of deer present at time 1 measured in years since the herd was introduced on a certain wildlife reserve has been determined by ecologists to be given by the function N=12.360.03+0.55t Figure1 a. How many deer were initially on the reserve? b. Calculate N(10) and explain the meaning of the number you have calculated. c. Express the number of deer present after 15 years using functional notation, and then calculate it. d. How much increase in the deer population do you expect from the 10th to the 15th year?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. 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. 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_forward
- Reminder Round all answers to two decimal places unless otherwise indicated. The Dangers of Smoking Cigarette smoke contains any number of unhealthy substances, cyanide among them. One study modeled cyanide in the bloodstream after smoking a cigarette using C=0.1+0.3t0.6e0.17t, where C is the concentration of cyanide in the bloodstream, measured in nanograms per deciliter, and t is the time, in minutes, since smoking a cigarette. a. Make a graph of the concentration of cyanide during the first hour after smoking a cigarette. Add the line corresponding to the target level of 0.3 nanogram per deciliter. b. During which period is the concentration of cyanide 0.3 nanogram per deciliter or higher?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_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. Wages A worker is reviewing his pay increases over the past several years. The table below shows the hourly wage W, in dollars, that he earned as a function of time t, measured in years since the beginning of 2000. Time t Wages W 1 15.30 2 15.60 3 15.90 4 16.25 a. By calculating ratios, show that the data in this table are exponential. Round the quotients to two decimal places b. What is the yearly growth factor for the data? c. The worker can't remember what hourly wage he earned at the beginning of 2000. Assuming that W is indeed an exponential function, determine what that hourly wage was? d. Find a formula giving an exponential model for W as a function of t. e. What percentage raise did the worker receive each year? f. Given that prices increased by 26 over the decade of the 2000s your model to determine whether the workers wage increases kept pace with inflation.arrow_forwardReminder Round all answers to two decimal places unless otherwise indicated. Logistic Formula A population grows according to the logistic model. N=251+0.5e1.4t where t is measured in years and N is measured in thousands. a. What is r for this population? b. What is the environmental carrying capacity K? c. This population is subject to harvesting. What is the optimum yield level?arrow_forwardReminder Round all answers to two decimal places unless otherwise indicated. Making an Exponential ModelShow that the accompanying data are exponential and find a formula for an exponential model. t f(t) t f(t) 0 3.80 3 4.27 1 3.95 4 4.45 2 4.11 5 4.62arrow_forward
- Functions and Change: A Modeling Approach to Coll...AlgebraISBN:9781337111348Author:Bruce Crauder, Benny Evans, Alan NoellPublisher:Cengage Learning