Chapter 7 Exponential and Logarithmic Functions Review Packet

Transcription

1 Non-Calculator Chapter 7 Exponential and Logarithmic Functions Review Packet Possible topics: Graphing exponential and logarithmic functions (and their transformations), switching between logarithmic and exponential form, evaluating logarithms (can use change of base formula with common base or rewrite in exponential form to evaluate see #3 on review), finding inverses of exponential/logarithmic equations, rewriting logarithms (expanding or as a single logarithm), solving exponential equations (with a common base), logarithmic equations. 1. Graph each parent function and their transformation on the same axes. Be sure to include the asymptotes. Include at least 5 points on your curve. Show your table of values for the parent function. (pg. 5 in notes, graphing by hand worksheet) a. Parent: y = 2 x b. Parent: y = log 3 x Transformation: y = 1 2 2x Transformation: y = log 3 (x 2) + 1 Description of Transf: Description of Transf: 2. Describe how the graph of each function compares with the graph of the parent function. (pg. 5 in notes, graphing by hand worksheet, warmup from 2/3) a. log 4 (x 2) + 3 b. y = 1 3 ex+2 c. y = 3 2 x 5 1

2 3. Evaluate each logarithm. (pg. 10 in notes, pg. 14 in notes top of page) a. log 6 36 b. log 3 27 c. log 8 16 d. log 81 9 e. log f. log Find the inverse of each function below. (pg. 12 in notes) a. y = 5 x b. y = log 2 32x c. y = ln x 5. Rewrite each expression as a single logarithm. Simplify when possible. (pg. 12 & 18 in notes) a. log 3 18 log 3 6 b. 2ln5 + ln4 c. 2log 2 x log log 216 d. 1 2 (log x4 + log x y) 3log x z 6. Expand each logarithm. Simplify when possible. (pg. 13 in notes) a. log 7 49xyz b. log a2 b 3 c 4 c. log 4 5 x d. log10m 4 n 2 2

3 7. Solve each exponential equation. (pg. 15 in notes top of page) a. 9 x = 81 b. 16 3x = 8 c. 64 6x = What is the solution of each logarithmic equation? (pg. 17 in notes) a. log 4x = 2 b. log 18 log 9x = 1 c. log 2x + log x = 2 9. Write each equation in logarithmic form. (pg. 9 in notes bottom) a. 7 3 = 343 b. ( 2 3 ) 3 = 27 c. 2 4 = Write each equation in exponential form. (pg. 10 in notes top) a. log 2 8 = 3 b. ln e 2 = 2 c. log 9 3 = 1 2 With Calculator Possible topics: exponential growth/decay word problems, continuously compounded interest, half-life of a substance, ph of a substance, exponential model for given set of data (regression on calculator), change of base formula, exponential equations (with different bases), logarithmic equations, natural logarithm and e x equations. 11. Suppose you deposit $1000 in a savings account that pays interest at an annual rate of 5%. No money is added or withdrawn from the account. (pg. 4 in notes) a. What is the value of r (the growth rate)? What equation models this situation? b. How much will be in the account after 5 years? 13 years? c. How many years will it take for the account to contain $2500? 3

4 12. Write an exponential function to model each situation. Then answer each question. a. A new car costs $20,000 and depreciates 25% each year. What is the value of r, (the decay rate)? How much is in the account after 4 years? (pg. 4 in notes) b. A parent increases a child s allowance by 15% each year. If the allowance is $3 now, how many years will it take to reach $15. Round to the nearest year. (pg. 4 in notes) 13. A homeowner is planting hedges and begins to dig a 3-ft-deep trench around the perimeter of his property. After the first weekend, the homeowner recruits a friend to help. After every succeeding weekend, each differ recruits another friend. One person can dig 405 ft 3 of dirt per weekend. The figure at the right shows the dimensions of the property and the width of the trench. a. Determine the volume of dirt that must be removed for the trench. b. Write an exponential function to model the volume of dirt remaining to be shoveled after x weekends. Then, use the model to determine how many weekends it will take to complete the trench. 14. You put $2000 into an account earning 4% interest compounded continuously. Find the amount in the account at the end of 8 years. (pg. 6 in notes) 4

5 15. In 2007, there were 1570 alligators in a wildlife refuge. In 2008, the population had increased to approximately 1884 alligators. If this trend continues and the alligator population is increasingly exponentially, how many alligators will there be in 2017? Round to the nearest alligator. (pg. 4 bottom of notes) 16. Water has a ph of 7. Find the concentration of hydrogen ions [H + ] using the equation ph = log[h + ]. (pg. 11 in notes) 17. Evaluate each exponential equation without graphing (algebraically). Round to the thousandths place. (pg , 19 in notes) a. 5 2x = 24 b. 4 x 3 = 12 c. 3 3x = 28 d. e x+2 = 12 e. 4e 2x = 20 f. e 3x + 3 = 9 5

6 18. Evaluate each logarithmic equation without graphing (algebraically). Round to the thousandths place. (pg in notes) a. ln 2x = 4 b. ln(3x + 4) 2 = 6 c. ln(3x 2) = 1 d. log 3x 2 log 6x = 2 e. log(x 3) + log x = 1 f. log 2x = What is the value of each expression? Hint: Remember the change of base formula. (pg. 13 in notes) a. log 7 25 b. log 12 4 c. log As a town gets smaller, the population of high school students decreases by 6% each year. The senior class has 160 students now. In how many years will it have about 100 students? Write an equation. Then solve the equation algebraically (without graphing). Round to the nearest year. 6