Determine whether the set of data displays exponential behavior.

Size: px

Start display at page:

Download "Determine whether the set of data displays exponential behavior."

Briana Barber
6 years ago
Views:

1 NAME DATE PERIOD,..;.-.. Study 0-5 Guide and Intervention (continued) ExponenValFuncVons Identify Exponential Behavior It is sometimes useful to know if a set of data is exponential. One way to tell is to observe the shape of the graph. Another way is to observe the pattern in the set of data. Determine whether the set of data displays exponential behavior. x Y Method : Graph the Data The graph shows rapidly decreasing values ofy as x increases. This is characteristic of exponential behavior. Method 2: Look for a Pattem The domain values increase by regular intervals of 2, while the range values have a common factor of t. Since the domain values increase by regular intervals and the range values have a common factor, the data are probably exponential. x Determine whether the data in each table display exponential behavior. Explain why or why not.. x Y ~= ~ 3.= ~ 4. x Y x x Y Y " Glencoe/McGraw-Hili 604 Glencoe Algebra

2 !~',;: '"i'-.':"',... t; ';~;'~(J NAME 0-6 Practice DATE Growth and Decay PERIOD COMMUNICATIONS For Exercises and 2, use the following information. Commercial non-music radio stations increased at an average annual rate of 3.% from 996 to Commercial radio stations in this format numbered 262 in 996. Sourte: MStreet Corporiltion, Nashville, TN. Write an equation for the number of radio stations for t years after 996. If the trend continues, predict the number of radio stations in this format for the year INVESTMENTS Determine the amount of an investment if $500 is invested at an interest rate of 4.25% compounded quarterly for 2 years. 4. INVESTMENTS Determine the amount of an investment if $300 is invested at an interest rate of 6.75% compounded semiannually for 20 years. 5. HOUSING The Greens bought a condominium for $0,000 in Ifits value appreciates at an average rate of 6% per year, what will the value be in 2005? DEFORESTATION For Exercises 6 and 7, use the following information. During the 990s, the forested area of Guatemala decreased at an average rate of.7%. ~e:~.worldb~n~o~ 6. If the forested area in Guatemala in 990 was about 34,400 square kilometers, write an equation for the forested area for t years after If this trend continues, predict the forested area in BUSINESS A piece of machinery valued at $25,000 depreciates at a steady rate of 0% yearly. What will the value of the piece of machinery be after 7 years? 9. TRANSPORTATION A new car costs $8,000. It is expected to depreciate at an average rate of 2% per year. Find the value of the car in 8 years. 0. POPULATION The population of Osaka, Japan declined at an average annual rate of 0.05% for the five years between 995 and If the population of Osaka was,03,000 in 2000 and it continues to decline at the same rate, predict the population in Glencoe/McGraw-Hili 62 Glencoe Algebra

3 NAME DATE 0-6 Study Guide and Intervention Growth and Decay PERIOD Exponential Growth Population increases and growth of monetary investments are examples ofexponential growth. This means that an initial amount increases at a steady rate over time. Exponential Growth The general equation for exponential growth is y = C( + r)l. y represents the final amount. C represents the initial amount. r represents the rate of change expressed as a decimal. t represents time. -exam ~ POPULATION The population ofjohnson City in 995 was 25,000. Since then, the population has grown at an average rate of 3.2% each year. a. Write an equation to represent the population of Johnson City since 995. The rate 3.2% can be written as 0.03 y =: e(l + r)t y :::: 25,000( Y y :::: 25,000(.032)t b. According to the equation, what will the population ofjohnson City be in the year 2005? In 2005, t will equal or 0. Substitute 0 for t in the equation from part a. y = 25,000(.032)0 t = 0 = 34,256 In 2005, the population ofjohnson City will be about 34,256...xam (2'. INVESTMENT The Garcias have $2,000 in a savings account. The bank pays 3.5% interest on savings accounts, compounded monthly. Find the balance in 3 years. The rate 3.5% can be written as The special equation for compound interest is A = p( + ~ r, where A represents the balance, P is the initial amount, r represents the annual rate expressed as a dedmal, n represents the number of times the interest is compounded each year, and t represents the number of years the money is invested. A = P(l + ~r A =: 2000( )36, 2 A = 2,000(.00292)36 A = 3, In three years, the balance of the account will be $3, POPULATION The population of the United States has been increasing at an average annual rate of 0.9%. Ifthe population of the United States was about 284,905,400 in the year 200, predict the U. S. population in the year Soun:e: u. S. Census Bureau 3. POPULATION It is estimated that the population of the world is increasing at an average annual rate of.3%. Ifthe population of the world was about 6,67,007,000 in the year 200, predict the world population in the year oIme: u.s Census Bureau INVESTMENT Determine the amount ofan investment of $2500 ifit is invested at in interest rate of 5.25% compounded monthly for 4 years, 4. INVESTMENT Determine the amount of an investment of $00,000 if it is invested at an interest rate of 5.2% compounded quarterly for 2 years. GlencoelMcGraw-Hili 609 Glencoe Algebra

4 :;, NAME.. DATE PERIOD 0-6 Study Guide and Intervention (continued) H tie'.) Growth and Decay Exponential Decay Radioactive decay and depreciation are examples of exponential decay. This means that an initial amount decreases at a steady rate over a period of time. Exponential Decay The general equation for exponential decay is y =0 C( - r)t. Y represents the final amount. C represents the initial amount., represents the rate of decay expressed as a decimal. t represents time. DEPRECIATION The original price of a tractor was $45,000. The value of the tractor decreases at a steady rate of 2% per year. a. Write an equation to represent the value of the tractor since it was purchased. The rate 2% can be written as 0. y = C( - r) t General equation for exponential decay y = 45,000(- 0.2)t C= 45,OOOandr= 0.2 y = 45,000(O.88)t Simplify. b. What is the value of the tractor in 5 years? y = 45,000(O.88)t Equation for decay from part a y = 45,000(0.88)5 t = 5 Y = 23, Use a calculator. In 5 years, the tractor will be worth about $23, POPULATION The population of Bulgaria has been decreasing at an annual rate of.3%. If the population of Bulgaria was about 7,797,000 in the year 2000, predict its population in the year elRte: U. S. Census Bureau DEPRECIATION Carl Gossell is a machinist. He bought some new machinery for about $25,000. He wants to calculate the value of the machinery over the next 0 years for tax purposes. Ifthe machinery depreciates at the rate of 5% per year, what is the value of the machinery (to the nearest $00) at the end of 0 years? 3. ARCHAEOLOGY The half-life of a radioactive element is defined as the time that it takes for one-half a quantity of the element to decay. Radioactive Carhon-4 is found in all living organisms and has a half-life of 5730 years. Consider a living organism with an original concentration of Carbon-4 of 00 grams. a. If the organism lived 5730 years ago, what is the concentration of Carbon-4 today? b. Ifthe organism lived,460 years ago, determine the concentration ofcarbon-4 today. 4. DEPRECIATION A new car costs $32,000. It is expected to depreciate 2% each year for 4 years and then depreciate 8% each year thereafter. Find the value of the car in 6 years. Glencoe/McGraw-Hili 60 Glencoe Algebra

5 Name: Page ) What is the simple interest, to the nearest douar, on $620 ifthe money is invested at 7% tor 5 months? A) $27 B) $8 C) $8J D) $2 2) Caitlin invested $2,300. In the first year she earned 5% interest and in the second year she earned 8% interest. How much money did she have at the end ofthe second year? A) $2, B) $2, C) $2, D) $2, ) Tomasa invested her money in an account paying 7.5% interest annually. Ifshe earned $40.50 simple interest for one year, then how much did she invest? A) $ B) $ C) $ D) $ ) [$3,000 is invested at 5% and $6,000 is invested at 'JOIO, what is the total annuaj income from both investments?

6 Name: ID: A Solve the problem ofexponential growth. 25. In 969 the Antique Automobile Club of America had 23,000 members. It grew an average of5% per year through 985. Assuming this continued what would the membership be in 2004? a. ]2,000 c. 27,000 b. 78,000 d. 5, According to the U.S. Census Bureau, the population ofcalifomia in 2000 was 33.8 million. This is a 3.8% increase over the 990 count. Assuming this continued what would the population be in 2020? a million c million b million d million Solve the equation ofexponential decay. 27. A car sells for $25,000. Ifthe rate ofdepreciation is 5%, what is the value of the car after 7 years? a. $8000 c. $7400 b. $9400 d. $ According to the U.S. Census Bureau, the District of Columbia's population in 2000 was 572,000. In the 990 census the population was 607,000. What was the rate ofchange of the population from one census to the next? a. 8% c. 3% b. 6% d. % 29. According to the Bureau of Labor Statistics, the number of fanners and ranchers is expected to decline 250/0 from 2000 to 200. The number of farmers and ranchers was,294,000 in Assuming this continued what would the number offarmers and ranchers be in 2040? a. 600,000 c. 400,000 b. 300,000 d. 800, According to US Citizenship and Immigration Statistics, the number of Asian immigrants to the United States was 342,000 in 200 This is a decline of 3% from the previous year. Assuming this continued what would the number of Asian immigrants be in 200? a. 277,000 c. 268,000 b. 29],000 d. 284,000 Find the next three terms in the geometric sequence. 3. 4, 2, 36, 08,... a. 324,972,296 c. 322,966,2898 b. 08,324,972 d. 324, 944,

7 Name: ID: A LU ~ a. No; the domain values are not at regular intervals. b. Yes; the domain values are at regular intervals and the range values have a common factor c. Yes; the domain values are at regular intervals and the range values have a common factor d. No; the domain values are at regular intervals and the range values have a common sum 9. EE =~ a. No; the domain values are at regular intervals and the range values have a common sum b. No; the domain values are not at regular intervals. c. Yes; the domain values are at regular intervals and the range values are the same as the domain values. d. Yes; the domain values are at regular intervals and the range values have a common sum -~---IEB-:- EEI--! ~-EE~-~a. No; the domain values are at regular intervals and the range values have a common sum b. No; the domain values are not at regular intervals. c. No; the domain values are at regular intervals and the range values have no common factor. d. Yes; the domain values are at regular intervals and the range values have a common sum EEl O~5 EB-i---ll..--;-;-I a. Yes; the domain values are at regular intervals and the range values have a common factor 8. b. Yes; the domain values are at regular intervals and the range values have a common factor 4. c. No; the domain values are not at regular intervals. d. No; the domain values are at regular intervals and the range values have a common factor 4. 7

EXPONENTIAL FUNCTIONS GET A GUIDED NOTES SHEET FROM THE BACK!

EXPONENTIAL FUNCTIONS GET A GUIDED NOTES SHEET FROM THE BACK! EXPONENTIAL FUNCTIONS An exponential function is a function with a variable in the exponent. f(x) = a(b) x EXPONENTIAL FUNCTIONS Parent graphs