Concept explainers
Reminder Round all answers to two decimal places unless otherwise indicated.
APR and APY Recall that financial institutions sometimes report the annual interest rate that they offer on investments as the APR, often called the nominal interest rate. To indicate how an investment will actually grow, they advertise the annual percentage yield, or APY. In mathematical terms, this is the yearly percentage growth rate for the exponential function that models the account balance. In this exercise and the next, we study the relationship between the APR and the APY. We assume that the APR is
To determine the APY when we know the APR, we need to know how often interest is compounded. For example, suppose for the moment that interest is compounded twice a year. Then to say that the APR is
a. | What is the yearly growth factor if interest is compounded four times a year? |
b. | Assume that interest is compounded
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c. | What is the yearly growth factor if interest is compounded daily? Give your answer to four decimal places/ |
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Functions and Change: A Modeling Approach to College Algebra (MindTap Course List)
- ReminderRound all answers to two decimal places unless otherwise indicated. Inflation An economist tracks the price of a certain item at the beginning of several years and compiles the following table. Years Price, in dollars 2013 265.50 2014 273.47 2015 281.67 2016 290.12 a. Show that the price is growing as an exponential function. b. Find an exponential model for the data. c. At the beginning of some year, the price will surpass 325. Use your model to determine which year.arrow_forwardReminder Round all answers to two decimal places unless otherwise indicated. Long-Term Population Growth Although exponential growth can often be used to model population growth accurately for some periods of time, there are inevitably, in the long term, limiting factors that make purely exponential models inaccurate. From 1790 to 1860, the U.S. population could be modeled by N=3.931.03tmillion people, where t is the time in years since 1790. If this exponential growth rate had continued until today, what would be the population of the United States have been in 2015? Compare your answer with the actual population of the United States in 2015, which was about 323million.arrow_forwardReminder Round all answers to two decimal places unless otherwise indicated. U.S Investment Abroad In 1980, direct U.S. business investment abroad was about 13.5 billion dollars. From 1980 through 2010, that investment grew at an average annual rate of 11.24. a.Make an exponential model that shows the U.S. direct investment aboard A, in billions of dollars, t years after 1980. b.From 1980, how long did it take for U.S. investments abroad to double? c.According to the model, how long would it take from 2010 for investments abroad to double the level present in 2010?arrow_forward
- Reminder Round all answers to two decimal places unless otherwise indicated. Mobile Phones According to one source, the amount of data passing through mobile phone networks doubles each year. a. Explain why the amount of data passing through mobile phone networks is as exponential function of time. b. Use D0 for the initial amount of data, and find a formula that gives the data D as an exponential function of the time t in years. c. If this trend continues, how long will it be before the amount of data is 100 times its initial value?arrow_forwardReminder Round all answers to two decimal places unless otherwise indicated. Gray Wolves in MichiganGray wolves recolonized in the Upper Peninsula of Michigan beginning in 1990. Their population has been documented as shown in the following table. 56 a.Explain why one expect an exponential model to be appropriate for these data. b.Find an exponential model for the data given. Year Wolves 1990 6 1991 17 1992 21 1993 30 1994 57 1995 80 1996 116 1997 112 1998 140 1999 174 2000 216 c.Graph the data and the exponential model. Would it be better to use a piecewise-defined function? d.Find an exponential model for 1990 through 1996 and another for 1997 through 2000. e.Write a formula for the number of wolves as a piecewise-defined function using the two exponential models. Is the combined model a better fit?arrow_forwardReminder Round all answers to two decimal places unless otherwise indicated. How Fast Do Exponential Functions Grow? At age 25, you start to work for a company and are offered two rather fanciful retirement options. Retirement Option 1 When you retire, you will be paid a lump sum of 25,000 for each year of service. Retirement Option 2 When you start to work, the company will deposit 10,000 into an account that pays a monthly interest rate of 1. When you retire, the account will be closed and the balance given to you. Which retirement option is more favorable to you if you retire at age 65? Which retirement option is more favorable if you retire at age 55?arrow_forward
- Reminder Round all answers to two decimal places unless otherwise indicated. Energy Requirements for India In 2009, India consumed 20 exajoules of energy from all sources. one exajoule is 1018joules. It is anticipated that energy requirements for India will increase by 8 per year for the foreseeable future. a.Make an exponential model for India that shows energy requirements E, in exajoules, t years after 2009. b.What are the expected energy requirements for India in 2030?arrow_forwardReminder Round all answers to two decimal places unless otherwise indicated. Gold Prices During the period from 2003 through 2010, gold prices doubled every 3years approximately. a.What was the yearly growth factor for the price of gold during this period? b.Explain in practical terms the meaning of the growth factor you found in part a.arrow_forwardReminder Round all answers to two decimal places unless otherwise indicated. Solar Panels In 2007, there were about 3.8gigawatts of solar photovoltaic installations. From 2007 through 2014, the industry showed exponential growth factor of 1.45. a.Make an exponential; model that shows the photovoltaic installations P, in gigawatts, at a time tyears after 2007. b.Use this model to estimate the photovoltaic installations in 2006.arrow_forward
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- Functions and Change: A Modeling Approach to Coll...AlgebraISBN:9781337111348Author:Bruce Crauder, Benny Evans, Alan NoellPublisher:Cengage Learning