#2. Be able to identify what an exponential decay equation/function looks like.

Transcription

1 1 Pre-AP Algebra II Chapter 7 Test Review Standards/Goals: G.2.a.: I can graph exponential and logarithmic functions with and without technology. G.2.b.: I can convert exponential equations to logarithmic form and logarithmic equations to exponential form. A.REI.11.: I can recognize and use function notation to represent exponential equations. A.CED.1.: I can create exponential equations and inequalities and use them to solve problems. F.IF.7e.: I can graph logarithmic functions, showing intercepts and end behavior. F.IF.8b.: I can use the properties of exponents to interpret expressions for exponential functions. F.LE.4.: I can recognize the law and properties of logarithms, including change of base. F.IF.7.e.: I can graph exponential functions showing both their intercepts and end behavior A.CED.2.: I can create and/or solve exponential equations with two variables. F.IF.8.: I can write an exponential function utilizing transformations that will affect its graph. A.REI.11.: I can solve real-life problems using exponential equations. Recognizing exponential growth vs. exponential decay. Be able to identify what an exponential growth equation/function looks like Be able to identify the y-intercept in an exponential equation. #1. Write the standard form here and be able to identify its parts and how its graph will look: #2. Be able to identify what an exponential decay equation/function looks like. #3. Be able to distinguish what the graph of growth vs. decay functions look like. o What type of function is shown: f(x) = 5? o Which of the following is an exponential growth function? #1. M(t) = OR #2. M(t) = 9.0 Use the properties of logarithms to condense the following expression as much as possible, writing the answer as a single term with a coefficient of 1. All exponents should be positive. #4. #5. #6. 4 ln 7 ln 9 #7. 2 log log 3

2 2 Use the change of base formula and your calculator to evaluate the following logarithmic expressions: Round your answer to TWO decimal places. #8. #9. #10. #11. Write the exponential equation in its logarithmic form. #12. What property is being illustrated below: Compare each function as a transformation of its parent function. (Identify its transformations.) State the y-intercept of each. #13. y = -5 (7) x #14. y = (9) x #15. y = -2 e x -5 1 Compare each function as a transformation of its parent function. (Identify its transformations.) Additionally, state the domain and range of each. #16. y = - 7 ln (x 7) #17. y = - ¾ log 2 x + 14 #18. y = 0.75 log 4 (x +1) 6

3 3 #19. Consider the following: f(x) = a. Name the domain and range of the function: b. Find a formula for the inverse, if possible. c. Name the domain and range for the inverse. #20. Consider the following: f(x) = a. Name the domain and range of the function: b. Find a formula for the inverse, if possible. c. Name the domain and range for the inverse.

4 4 STEM PROBLEMS: #21. Consider the following situation: A certain species of deer is to be introduced into a forest, and wildlife experts estimate the population will grow according to P(t) = ( ) number of years from the time of introduction. a. What is the TRIPLING TIME for this population of deer? where t represents the b. How long will it take for the population to reach 6822 deer, according to this model? #22. Mr. Andersen put $1000 into an account that earns 4.5% annual interest. The interest is compounded annually and there are no withdrawals. How much money will be in the account at the end of 30 years? #23. A manufacturer bought a new rolling press for $48,000. It has depreciated in value at an annual rate of 15%. What is its value 5 years after purchase? Round to the nearest hundred dollars.

5 5 #24. In June, a rural South American town was hit by an earthquake with a magnitude of 7.9 on the Richter scale. The same town was hit by another earthquake with a magnitude of 6.1 in August. How many times more intense was the earthquake in June? Use the formula: to solve the problem. #25. Given the following problem. The concentration of a certain drug in the bloodstream after minutes is given by the formula What is the concentration after 20 minutes? Round to 3 decimal places. #26. Given the following problem. Dolores invests $7100 in a new savings account which earns 5.3% annual interest, compounded continuously. What will be the value of her investment after 3 years? Round to the nearest cent.

6 #27. Consider the following: a. What is the vertex of this quadratic? b. What is the axis of symmetry? c. What is the minimum or maximum value? d. What is the domain and range of this function? e. What is the y-intercept? f. What is the discriminant value and how many real and how many imaginary solutions will it have? g. What are the solutions/x-intercepts to the equation? 6

7 #28. Consider the graph of the function:, which has one x-intercept at (-4, 0). Find all the other zeros of the function algebraically. Show your work. 7

8 8 #29. A certain polynomial can be written in factored form as: a. What are the zeros? b. What is the degree of the function? c. How many zeros are real; how many are imaginary? d. How many distinct real zeros are there? e. How many x-intercepts would the function have? #30. Consider the functions: g(x) = a. What is the exact value of f(-10)? Simplify your answer completely. Show your work. b. What is the domain of g(x)? Show your work.