Advanced Algebra Chapter 5C LOGARITHMIC FUNCTIONS Name Period Date Compound Interest Revisited - Homework SET UP AN EQUATION OR AN EXPRESSION FOR EACH PROBLEM. SHOW ALL THE NECESSARY WORK TO SOLVE YOUR EQUATIONS. GIVE BOTH EXACT ANSWERS AND APPROXIMATIONS ROUNDED TO THE NEAREST HUNDREDTH SHOW ALL YOUR WORK ON A SEPARATE SHEET OF PAPER. You want to invest $500 in an account that earns 7.75% interest. How much money will the account be worth after five years if the interest is compounded: Yearly? Semi-annually? Quarterly? Monthly?. Matt wants to have $500,000 in his savings account when he retires. He deposits $5,000 into an account that earns 8% interest and is compounded quarterly. How long will it take him to reach his 3. Kelly bought a new Mercedes for $4,000 which depreciates at 5% per year. Jesse bought a new Ford for $36,000 which depreciates 9% per year. After 8 years, they both decided to sell their vehicles. a) What is the value of the Mercedes at that point? b) What is the value of the Ford? c) Find the total change in value for the Mercedes. d) Find the total change in value of the Ford. e) Which vehicle decreased more in value? 4. Joe invested $0,000 in the stock market. Due to the recession, Joe s stocks have decreased in value by 3% per year. If he has $8,000 in stocks now, how long ago did he make the investment? 5. Cindy wants to pay cash for a new car. She will need 50,000 for the car she wants. She deposits 30,000 into a special saving account that earns 6.5% interest that is compounded weekly. How long will she have to leave the money in the account before she can buy the new car? 6. Gerard receives $750 in graduation money and plans to put it into an account that earns 4% interest compounded semi-annually. How long will it take for the account balance to be $900, so he can buy a new computer?
7. Matt wants to have $500,000 in his savings account when he retires. He deposits $3,50 into an account that earns 6% interest and is compounded quarterly. How long will it take him to reach his 8. Ella bought a new cell phone years ago. If the phone depreciated at a rate of 0% yearly, and is currently worth $46, how much did she pay for the phone when it was new? 9. Mr. Jones invested $0,000 in stocks. Unfortunately, the stocks did not do well and after 3 years, they were only worth $8,000. What was the annual depreciation rate of the stocks? 0. The Houston Astrodome was the first baseball and football stadium to be completely enclosed. It was completed in 965 at a cost of 45.35 million dollars. Construction costs have increased by approximately 6% each year since 965. How much would it cost to build the Astrodome today? Review Questions:. Graph the function y = log 7 x plotting at least 5 points. Clearly show and label any asymptote(s) on your graph. x y Equation of asymptote: In -4, evaluate each expression WITHOUT using your calculator.. log 0.00 = 3. log 00 = 4. log 6 = In 5-7, solve the equations WITHOUT using your calculator. 5. log 4 x = 3 6. ln x = 4 7. log x 5 = 3 In 8-0, solve each equation. Express your answer as a power or in terms of logarithms. Then, if necessary, use a calculator to approximate your answers to the nearest hundredth. 8. 3 log(x) 4 = 9. ln(x) + 3 = 0. e (x+) 8 =
Advanced Algebra Chapter 5C LOGARITHMIC FUNCTIONS ANSWER KEY Compound Interest Revisited - Homework SET UP AN EQUATION OR AN EXPRESSION FOR EACH PROBLEM. SHOW ALL THE NECESSARY WORK TO SOLVE YOUR EQUATIONS. GIVE BOTH EXACT ANSWERS AND APPROXIMATIONS ROUNDED TO THE NEAREST HUNDREDTH SHOW ALL YOUR WORK ON A SEPARATE SHEET OF PAPER. You want to invest $500 in an account that earns 7.75% interest. How much money will the account be worth after five years if the interest is compounded: Yearly? Semi-annually? A = 500 ( + 0.0775 ) 5 76.0 dollars A = 500 ( + 0.0775 ) 5 73.7 dollars Quarterly? A = 500 ( + 0.0775 ) 4 4 5 733.9 dollars Monthly? A = 500 ( + 0.0775 ) 5 735.73 dollars. Matt wants to have $500,000 in his savings account when he retires. He deposits $5,000 into an account that earns 8% interest and is compounded quarterly. How long will it take him to reach his 500,000 = 5,000 ( + 0.08 4t 4 ) t = 4 log.0(0) = 4 log 0 37.8 years log.0 3. Kelly bought a new Mercedes for $4,000 which depreciates at 5% per year. Jesse bought a new Ford for $36,000 which depreciates 9% per year. After 8 years, they both decided to sell their vehicles. a) What is the value of the Mercedes at that point? A = 4,000 (.05) 8 7,00.4 dollars b) What is the value of the Ford? A = 36,000 (.09) 8 6,99.0 dollars c) Find the total change in value for the Mercedes. $3,799.76 drop d) Find the total change in value of the Ford. $9,070.9 drop e) Which vehicle decreased more in value? The Ford devaluated more than the Mercedes 4. Joe invested $0,000 in the stock market. Due to the recession, Joe s stocks have decreased in value by 3% per year. If he has $8,000 in stocks now, how long ago did he make the investment? 8,000 = 0,000 ( 0.03) t t = log 0.97 ( 4 5 ) = log (4 5 ) 7.33 years ago log 0.97
5. Cindy wants to pay cash for a new car. She will need 50,000 for the car she wants. She deposits 30,000 into a special saving account that earns 6.5% interest that is compounded weekly. How long will she have to leave the money in the account before she can buy the new car? 50,000 = 30,000 ( + 0.065 5t 5 ) t = 5 log.00 ( 5 3 ) = 5 log ( 3 ) log.00 6. Gerard receives $750 in graduation money and plans to put it into an account that earns 4% interest compounded semi-annually. How long will it take for the account balance to be $900, so he can buy a new computer? 900 = 750 ( + 0.04 ) t t = log.0 ( 6 5 ) = log (6 5 ) 4.60 years log.0 5 8.7 years 7. Matt wants to have $500,000 in his savings account when he retires. He deposits $3,50 into an account that earns 6% interest and is compounded quarterly. How long will it take him to reach his 500,000 = 3,50 ( + 0.06 4t 4 ) t = 4 log.05(6) = 4 log(6) 46.56 years log.05 8. Ella bought a new cell phone years ago. If the phone depreciated at a rate of 0% yearly, and is currently worth $46, how much did she pay for the phone when it was new? 46 = a ( 0.) a = 650 dollars 9. Mr. Jones invested $0,000 in stocks. Unfortunately, the stocks did not do well and after 3 years, they were only worth $8,000. What was the annual depreciation rate of the stocks? 8,000 = 0,000 ( r) 3 3 r = 9 0.035 so 3.5% 0 0. The Houston Astrodome was the first baseball and football stadium to be completely enclosed. It was completed in 965 at a cost of 45.35 million dollars. Construction costs have increased by approximately 6% each year since 965. How much would it cost to build the Astrodome today? A = 45.35 ( +.06) 5 885.48 million dollars
Review Questions:. Graph the function y = log 7 x plotting at least 5 points. Clearly show and label any asymptote(s) on your graph. x - - 0 y /49 /7 7 49 Equation of asymptote: x = 0 In -4, evaluate each expression WITHOUT using your calculator.. log 0.00 = 3. log 00 = 4. log 6 = -3-4 In 5-7, solve the equations WITHOUT using your calculator. 5. log 4 x = 3 6. ln x = 4 7. log x 5 = 3 x = 8 x = e 4 x = 5 In 8-0, solve each equation. Express your answer as a power or in terms of logarithms. Then, if necessary, use a calculator to approximate your answers to the nearest hundredth. 8. 3 log(x) 4 = 9. ln(x) + 3 = 0. e (x+) 8 = x = 0 5 = 00,000 x = e 0.4 x = ln(3) 0.0