ALGEBRA

7.00 1. (07.01) What is the solution to the equation 9(x – 2) = 27? (1 point) x = 2.5 x = 0.5 x = –0.5 x = 3.5 2. (07.01) What is the solution to the equation = 4(m – 3)? (1 point) m =– m =– m = m = 3. (07.01) The value of a dirt bike decreases by 15% each year. If you purchased this dirt bike today for $500, to the nearest dollar how much would the bike be worth 5 years later? (1 point) $84 $119 $164 $222 4. (07.01) What is the exponential function modeled by the following table? x f(x) 2 5 3 9 4 17 (1 point) f(x) = 2x f(x) = 2x + 1 f(x) = 3x f(x) = 3x + 1 5. (07.01) The frog population at a lake doubles every week. The population can be modeled by f(x) = 15(2)x and f(6) = 960. What does the 6 represent? (1 point) The population after six weeks The starting population The rate the population increases The number of weeks that have passed 6. (07.01) The amount of a radioactive isotope decays in half every year. The amount of the isotope can be modeled by f(x) = 346( )x and f(1) = 173. What does the 346 represent? (1 point) The starting amount of the isotope The amount of the isotope after one year The rate the isotope decreases The number of years that have passed 7. (07.01) The population of a species of rabbit triples every year. This can be modeled by f(x) = 4(3)x and f(5) = 972. What does the 5 represent? (1 point) The starting population of the rabbits The population of the rabbits after five years The rate the population increases The number of years that have passed 8. (07.01) A painting is purchased for $500. If the value of the painting doubles every 5 years, then its value is given by the function V(t) = 500 2t/5, where t is the number of years since it was purchased and V(t) is its value (in dollars) at that time. What is the value of the painting ten years after its purchase? (1 point) $1,000 $1,400 $1,800 $2,000 9. (07.01) Wes has been tracking the population of a town. The population was 3,460 last year and has been increasing by 1.35 times each year. How can Wes develop a function to model this? (1 point) f(x) = 3460(1.35)x where 1.35 is the rate of growth f(x) = (3460 • 1.35)x where 1.35 is the rate of growth f(x) = 1.35(3460)x where 3460 is the rate of growth f(x) = 3460(x)1.35 where 3460 is the rate of growth 10. (07.01) A savings account compounds interest, at a rate of 15%, once a year. Elizabeth puts $800 in the account as the principal. How can Elizabeth set up a function to track the amount of money she has? (1 point) A(x) = 800(15)x where 15 is the interest rate A(x) = 800(1 + .15)x where .15 is the interest rate A(x) = 800(.15)x where .15 is the interest rate A(x) = 800(1 + 15)x where 15 is the interest rate 11. (07.02) What is the logarithmic function modeled by the following table? x f(x) 9 2 27 3 81 4 (1 point) f(x) = logx3 f(x) = 3 log10x f(x) = x log103 f(x) = log3x 12. (07.02) If Denise wanted to create a function that modeled a base of 12 and what exponents were needed to reach specific values, how would she set up her function? (1 point) f(x) = x12 f(x) = log12x f(x) = 12x f(x) = logx12 13. (07.02) Express 64 = 4x as a logarithmic equation. (1 point) log4x = 64 log464 = x log644 = x log64x = 4 14. (07.02) Express 32 = x as a logarithmic equation. (1 point) log3x = 2 log32 = x log23 = x log2x = 3 15. (07.02) What is the solution of log2x + 3125 = 3? (1 point) x = x = 1 x = x = 4 16. (07.02) What is the solution of log3x – 725 = 2? (1 point) x = –2 x = 2 x = 3 x = 4 17. (07.03) Which of the following is equivalent to log432? (1 point) 0.4 2.5 1.726 8 18. (07.03) Which of the following is equivalent to log840 rounded to three decimal places? (1 point) 0.599 0.898 1.564 1.774 19. (07.04) Given the exponential function A(x) = P(1 + r)x, what value for r will make the function a decay function? (1 point) r = 2.1 r = –0.1 r = 0 r = 0.1 20. (07.04) Given an exponential function for compounding interest, A(x) = P(1.01)x, what is the rate of change? (1 point) 0.01% 1% 1.01% 10% 21. (07.04) The function f(x) = 15(2)x represents the growth of a frog population every year in a remote swamp. Elizabeth wants to manipulate the formula to an equivalent form that calculates every half-year, not every year. Which function is correct for Elizabeth's purposes? (1 point) f(x) = 15( )2x f(x) = 15(22) f(x) = (2)x f(x) = 30(2)x 22. (07.04) Gabriel is using logarithms to solve the equation 52x = 27. Which of the following equations would be equivalent to his original expression? (1 point) 5 log 2x = log 27 2 log 5 = x log 27 x log 5 = 2 log 27 2x log 5 = log 27 23. (07.04) What is the solution to the equation 14 x – 3 = 21? (1 point) x ˜ –2.133 x ˜ –1.846 x ˜ 3.867 x ˜ 4.154 24. (07.04) What is the solution to the equation 9 –3x ˜7? (1 point) x = 0.376 x = 0.295 x = –0.295 x = –0.376 25. (07.04) What is the logarithmic form of the equation e3x ˜3247? (1 point) log3x3247 = e ln 3247 = 3x 3 logxe = 3247 ln 3x = 3247 26. (07.06) Which of the following represents the graph of f(x) = 2x + 2? (1 point) 27. (07.06) What function is represented below? (1 point) f(x) = f(x) = + 2 f(x) = f(x) = – 2 28. (07.06) Given four functions, which one will have the smallest y-intercept? f(x) g(x) h(x) j(x) Blake is tracking his savings account with an interest rate of 5% and a original deposit of $6. x g(x) 0 2 1 6 2 10 j(x) = 10(2)x (1 point) f(x) g(x) h(x) j(x) 29. (07.06) Given four functions, place them in order of their y-intercept, from highest to lowest. f(x) g(x) h(x) j(x) j(x) = 8(20)x Al is monitoring the decay of a population of fungi. It is reducing in half every four weeks. The population started at 5. x j(x) 1 8 2 4 3 2 (1 point) g(x), h(x), j(x), f(x) h(x), j(x), g(x), f(x) f(x), g(x), j(x), h(x) j(x), g(x), h(x), f(x) 30. (07.06) For the graphed exponential equation, calculate the average rate of change from x = –2 to x = 1. (1 point) 3 4 31. (07.06) For the graphed exponential equation, calculate the average rate of change from x = –3 to x = 0. (1 point) – – – 32. (07.06) What transformation has changed the parent function f(x) = 3(2)x to its new appearance shown in the graph below? (1 point) f(x) + 2 f(x) + 4 f(x + 2) f(x + 4) 33. (07.06) What transformation has changed the parent function f(x) = (.5)x to its new appearance shown in the graph below? (1 point) f(x) – 2 f(x + 2) f(x – 2) f(x) + 1 34. (07.07) Which of the following represents the graph of the function f(x) = log3(x – 2)? (1 point) 35. (07.07) What function is graphed below? (1 point) f(x) = log (x – 3) f(x) = log (x + 3) f(x) = log x + 3 f(x) = log x – 3 36. (07.07) Which graph represents the function f(x) = log10(x) + 2? (1 point) 37. (07.07) Using the graph of f(x) = log10x below, approximate the value of y in the equation 10y = 3. (1 point) y ˜ 0.48 y ˜ 0.01 y ˜ 1.48 y ˜ –2.01 38. (07.07) Using the graph of f(x) = log2x below, approximate the value of y in the equation 22y = 3. (1 point) y ˜ 4.01 y ˜ .79 y ˜ 1.58 y ˜ 0.47 39. (07.07) What transformation has changed the parent function f(x) = log2x to its new appearance shown in the graph below? (1 point) f(x + 3) f(x – 3) f(x) + 3 f(x) – 3 40. (07.07) What transformation has changed the parent function f(x) = log3x to its new appearance shown in the graph below? (1 point) f(x – 2) f(x + 2) f(x) – 2 f(x) + 2 41. (07.07) What transformation has changed the parent function f(x) = log5x to its new appearance shown in the graph below? (1 point) 2 f(x) f(x) – 2 f(x) + 2 –2 f(x) 42. (07.08) A heated piece of metal cools according to the function c(x) = (.5)x – 11, where x is measured in hours. A device is added that aids in cooling according to the function h(x) = –x – 3. What will be the temperature of the metal after five hours? (1 point) –8° Celsius 26° Celsius 32° Celsius 56° Celsius 43. (07.08) A population of flies grows according to the function p(x) = 5(2)x, where x is measured in weeks. A local spider has set up shop and consumes flies according to the function s(x) = 3x + 2. What is the population of flies after three weeks with the introduced spider? (1 point) 11 flies 19 flies 29 flies 40 flies 44. (07.08) A video game sets the points needed to reach the next level based on the function g(x) = 10(2)x – 1, where x is the current level. The hardest setting promises to multiply the points needed in each level according to the function h(x) = 2x. How many points will a player need on the hardest setting of level 5? (1 point) 10 points 160 points 1600 points 16000 points 45. (07.08) Given the function f(x) = 3x, find the value of f–1(81). (1 point) f–1(81) = 1 f–1(81) = 2 f–1(81) = 3 f–1(81) = 4 46. (07.08) Given the function f(x) = log2(x + 6), find the value of f–1(3). (1 point) f–1(3) = 2 f–1(3) = 3 f–1(3) = 9 f–1(3) = 18