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Splash Screen. Five-Minute Check (over Lesson 7–1) CCSS Then/Now New Vocabulary Key Concept: Property of Equality for Exponential Functions Example 1: Solve Exponential Equations Example 2: Real-World Example: Write an Exponential Function Key Concept: Compound Interest

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  1. Splash Screen

  2. Five-Minute Check (over Lesson 7–1) CCSS Then/Now New Vocabulary Key Concept: Property of Equality for Exponential Functions Example 1: Solve Exponential Equations Example 2: Real-World Example: Write an Exponential Function Key Concept: Compound Interest Example 3: Compound Interest Key Concept: Property of Inequality for Exponential Functions Example 4: Solve Exponential Inequalities Lesson Menu

  3. State the domain and range of y = –3(2)x. A. D = {x | x < 0}, R = {all real numbers} B. D = {x | x > 0}, R = {all real numbers} C. D = {all real numbers}, R = {y | y < 0} D. D = {all real numbers}, R = {y | y > 0} 5-Minute Check 1

  4. State the domain and range of A. D = {x | x < 0}, R = {all real numbers} B. D = {x | x > 0}, R = {all real numbers} C. D = {all real numbers}, R = {y | y < 0} D. D = {all real numbers}, R = {y | y > 0} 5-Minute Check 2

  5. The function P(t) = 12,995(0.88)t gives the value of a type of car after t years. Find the value of the car after 10 years. A. $3619.12 B. $4112.64 C. $8882.36 D. $9375.88 5-Minute Check 3

  6. The number of bees in a hive is growing exponentially at a rate of 40% per day. The hive begins with 25 bees. Which function models the population of the hive after t days? A.P(t) = 25(1.40)t B.P(t) = 25(1.60)t C.P(t) = 10t D.P(t) = 15t 5-Minute Check 4

  7. Content Standards A.CED.1 Create equations and inequalities in one variable and use them to solve problems. F.LE.4 For exponential models, express as a logarithm the solution to abct = d where a, c, and d are numbers and the base b is 2, 10, or e; evaluate the logarithm using technology. Mathematical Practices 2 Reason abstractly and quantitatively. CCSS

  8. You graphed exponential functions. • Solve exponential equations. • Solve exponential inequalities. Then/Now

  9. exponential equation • compound interest • exponential inequality Vocabulary

  10. Concept

  11. Solve Exponential Equations A.Solve the equation 3x = 94. 3x = 94 Original equation 3x = (32)4 Rewrite 9 as 32. 3x = 38 Power of a Power x = 8 Property of Equality for Exponential Functions Answer:x = 8 Example 1A

  12. Solve Exponential Equations B.Solve the equation 25x = 42x – 1. 25x = 42x – 1 Original equation 25x = (22)2x – 1 Rewrite 4 as 22. 25x = 24x – 2 Power of a Power 5x = 4x – 2 Property of Equality for Exponential Functions x = –2 Subtract 4x from each side. Answer:x = –2 Example 1B

  13. A. Solve the equation 4x = 643. A. 3 B. 9 C. 18 D. 27 Example 1A

  14. B. Solve the equation 32x = 95x – 4. A. 1 B. 2 C. 4 D. 5 Example 1B

  15. Write an Exponential Function A. POPULATIONIn 2000, the population of Phoenix was 1,321,045. By 2007, it was estimated at 1,512,986. Write an exponential function that could be used to model the population of Phoenix. Write x in terms of the numbers of years since 2000. At the beginning of the timeline in 2000, x is 0 and the population is 1,321,045. Thus, the y-intercept, and the value of a, is 1,321,045. When x = 7, the population is 1,512,986. Substitute these values into an exponential function to determine the value of b. Example 2A

  16. Write an Exponential Function y = abx Exponential function 1,512,986 = 1,321,045 ● b7 Replace x with 7, y with 1,512,986, and a with 1,321,045. 1.145 ≈ b7 Divide each side by 1,321,045. Take the 7th root of each side. 1.0196 ≈ b Use a calculator. Answer: An equation that models the number of years is y = 1,321,045(1.0196)x. Example 2A

  17. Write an Exponential Function B. POPULATIONIn 2000, the population of Phoenix was 1,321,045. By 2007, it was estimated at 1,512,986. Predict the population of Phoenix in 2013. y = 1,321,045(1.0196)x Modeling equation y = 1,321,045(1.0196)13 Replace x with 13. y ≈ 1,700,221Use a calculator. Answer: The population will be about 1,700,221. Example 2B

  18. A. POPULATIONIn 2000, the population of the town of Tisdale was 9,426. By 2007, it was estimated at 17,942. Write an exponential function that could be used to model the population of Tisdale. Write x in terms of the numbers of years since 2000. A.y = 9,426(1.0963)x – 7 B.y = 1.0963(9,426)x C.y = 9,426(x)1.0963 D.y = 9,426(1.0963)x Example 2A

  19. B. POPULATIONIn 2000, the population of the town of Tisdale was 9,426. By 2007, it was estimated at 17,942. Predict the population of Tisdale in 2012. A. 28,411 B. 30,462 C. 32,534 D. 34,833 Example 2B

  20. Concept

  21. Compound Interest An investment account pays 5.4% annual interest compounded quarterly. If $4000 is placed in this account, find the balance after 8 years. Understand Find the balance of the account after 8 years. Plan Use the compound interest formula. P = 4000, r = 0.054, n = 4, and t = 8 Example 3

  22. Compound Interest Formula P = 4000, r = 0.054, n = 4, and t = 8 Use a calculator. Compound Interest Solve Answer: The balance in the account after 8 years will be $6143.56. Example 3

  23. Compound Interest Check Graph the corresponding equation y = 4000(1.0135)4t. Use the CALC: value to find y when x = 8. The y-value 6143.6 is very close to 6143.56, so the answer is reasonable. Example 3

  24. An investment account pays 4.6% annual interest compounded quarterly. If $6050 is placed in this account, find the balance after 6 years. A. $6810.53 B. $7420.65 C. $7960.43 D. $8134.22 Example 3

  25. Concept

  26. Original equation Property of Inequality for Exponential Functions Subtract 3 from each side. Solve Exponential Inequalities Example 4

  27. Divide each side by –2 and reverse the inequality symbol. Answer: Solve Exponential Inequalities Example 4

  28. A.x < 9 B.x > 3 C.x < 3 D.x > 6 Example 4

  29. End of the Lesson

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