VIEWS: 22 PAGES: 2 POSTED ON: 10/17/2011
APPLYING EXPONENTIAL EQUATIONS TO SOLVE PROBLEMS APPRECIATION: y = a(1+r)t When finding the Initial When finding the amount, just plug into DEPRECIATION: y = a(1-r)t Final amount, just nt the correct formula, plug into the r simplify the right side COMPOUNDED GROWTH (MONEY): y a1 and then divide into the correct formula n and calculate! final amount! BACTERIA GROWTH OR DECAY COMPOUNDED CONTINUOUSLY y = aekt or y = aert y = Final Amount (F) ; a is the initial amount (A) ; r or k is the rate as a decimal (R); t is the time (T) n – number of times compounded Finding the FINAL amount Finding the Initial amount 1. The population of Johnson City in 1995 was 25,000. 5. Louisa read that the population of her town has Since then, the population has grown at an average rate increased steadily at a rate of 2% each year. Today, the of 3.2% each year. Write an equation to model the population of her town has grown to 68,735. Based on growth and find the population of Johnson City in the this information, what was to population of her town year 2005. 100 years ago? F – ________ R – ________________ A – _________ T – ________________ 6. Your parents gave you a car for your 16 th birthday. Once you finish college, you decide it is time to trade it in. Kelly Blue Book says it is worth $2125. It has 2. You buy a new computer for $2100. The value of depreciated at a rate of 7% for 6 years. How much did the computer decreases by about 50% annually. your parents pay for the car? Write an exponential decay model for the value of the computer. Use the model to estimate the value after 2 years. F – ________ R – ________________ 7. You want to have $2500 after 2 years. Find the A – _________ T – ________________ amount you should deposit for each of the situations described below: a) The account pays 2.25% annual interest compounded monthly. 3. You deposit $1600 in a bank account. Find the b) The account pays 2% interest compounded balance after 3 years for each of the following quarterly. situations: a) The account pays 2.5% compounded monthly. b) The account pays 1.75% annual interest compounded quarterly. c) The account pays 4% annual interest compounded yearly. F – ________ A – _________ 8. Dekorie has $3000 in an account in the bank that is R -- ________ compounded continuously at an interest rate of 2.1%. If N -- ________ she deposited the money 10 years ago, how much did T -- ________ she deposit? 4. Horatio opens a bank account that pays 2.3% annual interest compounded continuously. He makes an initial deposit of $10,000. What will be the balance of the account in 10 years? F -- _________ A -- __________ R -- __________ T -- __________ APPLYING EXPONENTIAL EQUATIONS TO SOLVE PROBLEMS When finding APPRECIATION: y = a(1+r)t When finding the time, the rate, divide DEPRECIATION: y = a(1-r)t divide by the initial by the initial r nt then take the log! and then take COMPOUNDED GROWTH (MONEY): y a1 Double means 2 = the “tth” root! n Triple means 3 = BACTERIA GROWTH OR DECAY 1 COMPOUNDED CONTINUOUSLY Half life means = y = aekt or y = aert 2 y = Final Amount (F) ; a is the initial amount (A) ; r or k is the rate as a decimal (R); t is the time (T) n – number of times compounded Finding the rate Finding the time 9. In a laboratory, an organism grows from 100 to 250 in 13. There are currently 850 students at the high school, 8 hours. What is the hourly growth rate in the growth which represents full capacity. The town plans an formula y a (1 r ) ? addition to house 400 more students. If the school t population grows at 7.8% per year, in how many years will the new addition be full? 10. A new car was purchased in 1990 for $14,000. 3 years later the car is valued at $5600. What is the rate of 14. A Global Positioning Satellite system uses satellite depreciation? information to locate ground position. Abu’s surveying firm bought a GPS system for $12,500. The GPS depreciated by a fixed rate of 6% and is now worth $8600. How long ago did Abu buy the GPS system? 11. In 1994, your parents opened a college savings account for you and deposited $5000 that is compounded monthly. When you graduate from high school in 2012 the account is worth $7837. What was 15. In 2001, Travis deposited $4000 in an account that the interest rate on the account, assuming they did not has 4.5% interest compounded quarterly. How many make any other deposits? years will it take his money to double? Triple? 16. A certain element decays at a rate of .012%. What 12. The element plutonium-239 is highly radioactive. is the elements’ half life? (Use the formula A A0 e ) kt Nuclear reactors can produce and also use this element. The heat that plutonium – 239 has helped to power equipment to the moon. If the half life of plutonium- 239 is 24, 360 years, what is the value of k for this element? (Use the formula A A0 e ) kt 17. The equation A A0 e describes the growth of the rt world’s population where A is the population at time t, A0 is the population a t = 0, and r is the annual growth rate. How long will it take a population of 6.5 billion to increase to 9 billion if the annual growth rate is 2%