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1 6 Chapter Review Review Ke Vocabular closed, p. 266 nth root, p. 278 eponential function, p. 286 eponential growth, p. 296 eponential growth function, p. 296 compound interest, p. 297 Vocabular Help eponential deca, p. 302 eponential deca function, p. 302 geometric sequence, p. 308 common ratio, p. 308 recursive rule, p. 312 Review Eamples and Eercises 6.1 Properties of Square Roots (pp ) Evaluate b 2 ac when a = 2, b = 2, and c = 5. b 2 ac = 2 2 ( 2)(5) Substitute. = Simplif. = 11 Factor. = 11 Product Propert of Square Roots = 2 11 Simplif. Evaluate the epression when = 3, =, and z = z 2. 2z z 6.2 Properties of Eponents (pp ) Simplif ( 3 ). Write our answer using onl positive eponents. ( 3 ) (3) = Power of a Quotient Propert = (3) = Definition of negative eponent 3 Power of a Product Propert = Simplif. Chapter Review 317

2 Simplif. Write our answer using onl positive eponents ( 2 ) 3 7. ( 2 5 ) Radicals and Rational Eponents (pp ) Simplif each epression. a = = 8 Rewrite and simplif. b /2 = 900 Write the epression in radical form. = Rewrite. = 30 Simplif. Simplif the epression / / 6. Eponential Functions (pp ) a. Graph =. Step 1: Make a table of values Step 2: Plot the ordered pairs Step 3: Draw a smooth curve through the points b. Write an eponential function represented b the graph. Use the graph to make a table of values The -intercept is 2 and the -values increase b a factor of 3 as increases b (, 162) (1, 6) (3, 5) (0, 2) (2, 18) So, the eponential function is = 2(3). 318 Chapter 6 Eponential Equations and Functions

3 11. Graph = 2() + 3. Describe the domain and range. Compare the graph to the graph of = 2(). Write an eponential function represented b the graph or table (3, 2) (2, 12) (1, 6) (0, 3) Solve the equation. Check our solution, if possible = = = Eponential Growth (pp ) The enrollment at a high school increases b % each ear. In 2010, there were 800 students enrolled at the school. a. Write a function that represents the enrollment of the high school after t ears. = a(1 + r) t Write eponential growth function. = 800( ) t Substitute 800 for a and 0.0 for r. = 800(1.0) t Simplif. b. How man students will be enrolled at the high school in 2020? The value t = 10 represents = 800(1.0) t Write eponential growth function. = 800(1.0) 10 Substitute 10 for t. 118 Use a calculator. 17. PLUMBER A plumber charges \$22 per hour. The hourl rate increases b 3% each ear. a. Write a function that represents the plumber s hourl rate (in dollars) after t ears. b. What is the plumber s hourl rate after 8 ears? Chapter Review 319

4 6.6 Eponential Deca (pp ) The table shows the value of a boat over time. Year, t Value, \$6000 \$800 \$380 \$3072 a. Determine whether the table represents an eponential growth function, an eponential deca function, or neither Year, t Value, \$6000 \$800 \$380 \$ As increases b 1, is multiplied b 0.8. So, the table represents an eponential deca function. b. The boat loses 20% of its value ever ear. Write a function that represents the value (in dollars) of the boat after t ears. = a(1 r) t Write eponential deca function. = 6000(1 0.2) t Substitute 6000 for a and 0.2 for r. = 6000(0.8) t Simplif. c. Graph the function from part (b). Use the graph to estimate the value of the boat after 8 ears. From the graph, ou can see that the -value is about 1000 when t = 8. So, the value of the boat is about \$1000 after 8 ears. Value (dollars) Value of a Boat 6000(0.8) t t Year Determine whether the table represents an eponential growth function, an eponential deca function, or neither DISCOUNT The price of a TV is \$1500. The price decreases b 6% each month. Write and graph a function that represents the price (in dollars) of the TV after t months. Use the graph to estimate the price of the TV after 1 ear. 320 Chapter 6 Eponential Equations and Functions

5 6.7 Geometric Sequences (pp ) a. Write the net three terms of the geometric sequence 2, 6, 18, 5,.... Use a table to organize the terms and etend the pattern. Position Term Each term is 3 times the previous term. So, the common ratio is Multipl a term b 3 to find the net term. The net three terms are 162, 86, and 158. b. Graph the geometric sequence 2, 12, 6, 3, 1.5,.... What do ou notice? Make a table. Then plot the ordered pairs (n, ). Position, n Term, The points of the graph appear to lie on an eponential curve (1, 2) (2, 12) (3, 6) (, 3) (5, 1.5) n Write the net three terms of the geometric sequence. Then graph the sequence , 9, 27, 81, , 12, 3, 3,... Write an equation for the nth term of the geometric sequence. 23. n Write a recursive rule for the sequence. 2. n , 8, 13, 18, 23, , 6, 12, 2, 8,... Chapter Review 321

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