Math Chapter 8 Test Review Key

Chapter 8 Test Review Algebra 1 CP Name: Key HR: ___ Simplify the expression. 1. (9x³y²)² 81x⁶y⁴ 2. -(2cd⁻³)³ -8c³d⁻⁹ -8c³/d⁹ 3. (a⁴b³) (ab⁷)⁵ a⁴b³ * a⁵b³⁵ a⁹b³⁸ 4. 25x³y² / 35xy⁵ 5x²/7y³ 5. 27x⁴y⁻¹ / (3x³y)² 27x⁴y⁻¹ / 9x⁶y² 3x⁻²y⁻³ 3 / x²y³ 6. 5 / w⁻¹ 5w³ 7. (2x³y²)⁴ / (5x⁻⁴y)⁴ 16x¹²y⁸ / 625x⁻¹⁶y⁴ 16x²⁸y⁴ / 625 8. (2ab²)⁴ / 6a⁻³b⁴ 16a⁴b⁸ / 6a⁻³b⁴ 8a⁷ 9. (64m⁻³)³ / 2m²n⁻³ 64³m⁻⁹ / 2m²n⁻³ 128m⁻¹¹n³ 128n³ / m¹¹ *growth when b > 1, decay when 0 < b < 1* Tell whether the table represents exponential growth or decay. Then write a rule for the function. 10. | x | -2 | -1 | 0 | 1 | 2 | |---|---|---|---|---|---| | y | 1/16 | 1/4 | 1 | 4 | 16 | y = 1 * (4)^x growth 11. | x | -2 | -1 | 0 | 1 | 2 | 3 | | y | 5/4 | 5/2 | 5 | 10 | 20 | 40 | y = 5 * (2)^x growth 12. | x | -2 | -1 | 0 | 1 | 2 | | y | 25 | 5 | 1 | 1/5 | 1/25 | y = 1 * (1/5)^x decay 13. | x | -2 | -1 | 0 | 1 | 2 | | y | 100 | 10 | 1 | 0.1 | 0.01 | y = 1 * (1/10)^x decay Circle whether the function represents exponential growth or decay. Graph the function. Identify its domain and range. 14. y = 5 * 2^x Growth Decay | x | -2 | -1 | 0 | 1 | 2 | |---|---|---|---|---|---| | y | 5/4 | 5/2 | 5 | 10 | 20 | D: all reals R: y > 0 15. y = 2 * (4/3)^x Growth Decay | x | -2 | -1 | 0 | 1 | 2 | |---|---|---|---|---|---| | y | 9/8 | 3/2 | 2 | 8/3 | 16/9 | D: all reals R: y > 0 16. y = 3^x Growth Decay | x | -2 | -1 | 0 | 1 | 2 | |---|---|---|---|---|---| | y | 1/9 | 1/3 | 1 | 3 | 9 | D: all reals R: y > 0 17. y = -3 * 2^-x Growth Decay | x | -2 | -1 | 0 | 1 | 2 | |---|---|---|---|---|---| | y | -3/4 | -3/2 | -3 | -12 | -48 | D: all reals R: y < 0 18. y = (1/2)^x Growth Decay | x | -2 | -1 | 0 | 1 | 2 | |---|---|---|---|---|---| | y | 4 | 2 | 1 | 1/2 | 1/4 | D: all reals R: y > 0 19. y = 2 * (1/5)^x Growth Decay | x | -2 | -1 | 0 | 1 | 2 | |---|---|---|---|---|---| | y | 50 | 10 | 2 | 2/5 | 2/25 | D: all reals R: y > 0 20. A business had $10,000 profit in 2000. Then the profit increased by 8% each year for the next 10 years. a) Write a function that models the profit in dollars over time.   P = 10,000(1 + 0.08)^t = 10,000(1.08)^t b) Use the function to predict the profit in 2009. P = 10,000(1.08)^9 ≈ $19,990.05 Tell whether the graph represents exponential decay or exponential growth. Then write a rule for the function. 21.   decay Rule: y = 3 * (3/4)^x 22. growth Rule: y = 2^x 23. You buy a computer for $3000. It depreciates at the rate of 20% per year. Find the value of the computer for the given year.   Value = 3000(1 - 0.20)^t = 3000(0.8)^t a) 1 year V = 3000(0.8)^1 = $2400 b) 3 years V = 3000(0.8)^3 = $1536 c) 5 years V = 3000(0.8)^5 = $898.88 Graph the function. Compare the graph with the graph of y = 4^x 24. y = -4^x Compare: reflection over x-axis 25. y = 3 * 4^x Compare: vertical stretch 26. A recent college graduate accepts a job at a law firm. The job has a salary of $32,000 per year. The law firm guarantees an annual pay increase of 3% of the employee's salary. a) Write a function that models the employee's salary over time. Assume that the employee receives only the guaranteed pay increase.   S = 32,000(1 + 0.03)^t b) Use the function to find the employee's salary after 5 years. S = 32,000(1.03)^5 ≈ $37,096.77 27. The value of a car is $18,000. The car depreciates (loses value) at a rate of about 16% annually. Find the approximate value of the car in 3 years.   V = 18,000(1 - 0.16)^3 ≈ $10,668.67 28. In the growth model, identify the growth rate, the growth factor, and the initial amount. y = 0.1(1.75)^t Growth rate: 75% Growth factor: 1.75 Initial amount: 0.1 29. In the decay model, identify the decay rate, the decay factor, and the initial amount. y = 4(0.97)^t Decay rate: 3% Decay factor: 0.97 Initial amount: 4