What You Need to Know for the Chapter 7 Test

Transcription

1 Score: /46 Name: Date: / / Hr: Alg 2C Chapter 7 Review - WYNTK CH 7 What You Need to Know for the Chapter 7 Test 7.1 Write & evaluate exponential expressions to model growth and decay situations. Determine if the function represents exponential growth or decay. 1. f (x) = 0.2(5) x 2. f (x) = 2(0.5) x 3. f (x) = ( ) x 4. Suppose that the number of bacteria in a culture was 1000 on Monday and the number has been increasing at a rate of 50% per day since then. A. Write a function representing the growth of the culture per day. B. Write and solve an equation to predict the number of bacteria in the culture the following Monday (which is days after the start.) 5. A new softball dropped onto a hard surface from a height of 25 inches, each rebound the ball s height decreases to 40% of the previous height. A. Write a function representing the rebound height for each bounce. B. Write and solve an equation (with algebra or a graph/table) to predict after how many bounces would a new softball rebound less than 1 inch? 7.2 Recognize and find inverses of relations and functions. Write the inverse, f -1 (x) of the following functions. 6. f (x) = 2x f (x) = x f (x) = 2x Pg. 1

2 7.3 Write equivalent forms for exponential and logarithmic functions. WITHOUT A CALCULATOR: Write the exponential equation in logarithmic form Write the logarithmic equation in exponential form Write, evaluate, and graph logarithmic functions. WITHOUT A CALCULAOTR: Evaluate using mental math. 13. log 2 (16) = log log ( 12) = log 1 2 ( ) = log( 0.001) = ( ) = Use properties to simplify logarithmic expressions. WITHOUT A CALCULATOR: Express as a single logarithm and evaluate log ( ) = log ( ) = WITHOUT A CALCULATOR: Express as a product and evaluate. 20. log log ( ) log ( ) WITHOUT A CALCULATOR: Simplify. = = 7.5 Translate between logarithms in any base. Evaluate, round to the nearest 100 th if necessary Pg. 2

3 7.5 Solve exponential and logarithmic equations and equalities. Solve for x x +2 = log log 3 (x + 2) = 5 log(16x 9) = log(25 x) 31. log x 15 log x 10 = log 2 x 2 = Use a graphing calculator to solve 5(3) x = 5510 Round to the nearest 10 th. 7.5 Solve problems involving exponential and logarithmic equations. 34. * Leave your answer as a power of 10. The energy released by an earthquake with magnitude of 4.2 would be ergs. Pg. 3

4 7.6 Simplify expressions involving e and natural logarithms. Simplify Solve equations and problems involving e or natural logarithms (compound interest & ½ life.) 38. * Round to the nearest cent. A = $ 7.6 Solve equations and problems involving e or natural logarithms (compound interest & ½ life.) 39. A. Use the natural decay function N(t) = N o e -kt, to find the decay constant, k for a substance that has a half-life of 1000 years. Round k, to 4 places after the decimal. K = B. Given that there was 100 g of the substance to start with, find how many years it would take for that 100 g sample to decay to a 10 g sample. Round to the nearest year grams Pg. 4

5 7.7 Describe the effects of changes in the coefficients of exponents and logarithmic functions. WITHOUT A CALCULATOR: Write each transformation function. 40. The function f(x) = log (x + 1) is reflected across the y-axis and translated down 4 units to create g(x). g(x) = 41. The function f(x) = -8 x-3 is reflected across the x axis and translated down 9 units and vertically stretched by a factor of 2 to create g(x). g(x) = 42. The function f(x) = 2log(x) + 9 is translated 15 units right and vertically compressed by a factor of 2 to create g(x). g(x) = 7.7 Transform exponential and logarithmic functions by changing parameters. 43. Graph the function: g(x) = 2 (x 2) 6 Describe/identify the asymptote. Tell how the graph is transformed from the graph of: g(x) = 2 x State the domain and range of g(x). x g(x) = 2 (x 2) 6 Domain of g(x) { } Range of g(x): { } Pg. 5

6 7.7 Transform exponential and logarithmic functions by changing parameters. Graph each function (on your calculator). Find the y-intercept and asymptote. Describe how the graph is transformed from the graph of the parent function. 44. g(x) = 4(2 x ) 45. g(x) = 1 log(x + 3) 2 y-intercept: (, ) Asymptote: Parent Function: f(x) = Transformations: y-intercept: (, ) Asymptote: Parent Function: f(x) = Transformations: 7.8 Model data by using exponential and logarithmic functions. Determine whether y is an exponential function of x. If so, find the constant ratio. Then use exponential regression to find a function that models the data f(x) = f(x) = 7.8 Use exponential and logarithmic models to analyze and predict. 46. Pg. 6