While observing the increase in the base cost of his cell phone bill each year, a student recorded the following data: January's Cell Phone Bill for the Past 4 years Year Base Rate on Bill $59.95 2 $61.75 3 $63.60 4 $65.51 Does the increase in price represent a linear or exponential function? O Linear, and the constant growth rate is $1.80 per year O Linear, and the growth factor is 1.03 per year O Exponential, and the constant growth rate is $1.80 per year Exponential, and the growth factor is 1.03 per yearA pine tree seedling has an initial height of 30 cm. It continually grows at a fixed rate, k, per year. If the tree is 365 cm tall in 10 years, based on the graphs below, what is the growth rate, k, to the nearest whole percent, of this pine tree? k=0.35 k=0.30 1100 -1000 k=0.40 -900 -800 -700 Height of tree -600 k=0.25 (In cm) -500 -400 -300 -200 -100 -6 8 9 10 11 12 13 14 15 16 17 18 19 --100 Number of Years 40% 35% 30% 25%Which of the following is an expression for the inverse of y = (8): ? O y = log: O y = log, 8 O y= -(8)* O y= (8)-* What is the inverse of y = logs (x) - 4? O y = logs (-x) - 4 O y = (6)# +4 O y = (6)+4 O y= -logg (x) +4 Express 53 = 125 in logarithmic form: O log, 5 = 125 log 125 5 = 3 10g 125 3 = 5 O log, 125 = 3What is the exact value of the exponential equation 25' 57 = 43? (I _ [0388 '4 5 n 2 '\\_4 = g r\". _ M '4 _ b _ 2 O z- blag! The number of hours, t that a bacteria spreads 10fold, can be modelled by the equation Bic) = 5900)\". There are 5 bacteria present initially,r and a biologist wishes to nd out how man}.r hours will lapse until there are 5600 bacteria present. What is the exact value for the number of hours elapsed, t, in the equation 5500 = sum\"? r\". e 135\" '4 _ 2log5 logll e, t: 2 l 112 O c: \"3 a 2 e_m.:;5~3ciu '4 _2log5l] Which one of the following equations solves the equation 50(10)' = 25 form? w _ log 10 log a O z = log 10 z = Lag; e, 10E _ Write the following expression as a single logarithm. log, B +log, D - 5log, E - log, A3 + 6 log, A O log ABD O log, 6A' BDES O log SA' BD E O log4 AABD GE Solve the logarithmic equation for a: log, (x + 7) + log, x = log, 8 O 3.5 O 7 O 1 O -8 If logs ? = 2 and 2 log, va = 1, then the value of * is O 81 O 9r 0 9 O 27The following data were recorded while observing the increase in the number of strawberry plants produced in a field for 2 different varieties, Plant A and Plant B, and are graphed below. |240 +220 --200 180 -160 140 Number of Plants -120 --100 Plant A 80 60 Plant B 40 -20 8 --20 Time(years) In the long term, which plant should the strawberry farmer grow to maximize the number of new plants produced?Plant B, because it has a greater percentage growth rate, which is graphically better in the long term O Plant A, because it has a greater percentage growth rate, which graphically is better in the long term O Plant B, because it has less plants to begin with, which is graphically better in the long term O Plant B, because the growth rate increases as time goes and becomes much higher than the growth rate of Plant A. Two competing passenger trains create a new marketing plan, charging passengers a fixed amount and then a rate per mile. Fast Track : $79.75 plus $0.30 a mile. Cheap Track: $179.50 plus $0.25 a mile. A one-way train ride from Miami to San Francisco is 2585 miles. If C is the cost of the ride, and M is the number of miles one-way, what is the equation for the cheapest option, and how much money will you save? O Fast Track, the equation is C = 79.75M + 0.30, and you save $149.70 O Cheap Track, the equation is C = 179.50M + 0.25, and you save $149.75 O Fast Track, the equation is C = 0.30M + 79.75, and you save $29.50 O Cheap Track, the equation is C = 0.25M + 179.50, and you save $29.50 The expression (216)=/3 is equivalent to: O (216)= - (216)3 O (6) O 6x O (6) 1Which of the following equations could describe the graph below? (1,0) O log 1 T (6) O log, IWhen a student was born: their parents invested $40300 in an investment guaranteed to increase by 3% per year. The logarithmic function y = 77,910; \"in\" can be used to determine the number of years: 1;, it takes for the investment to be worth x dollars. -90 Time in Years -80 4'0 -50 -50 -40 3o -20 -10 1 DO 20 00 30 4 DO SO 00 60 00 1'0 00 80 00 90 DO -20 Value oflnvcstmcnt (S) Approximately after how man},r years will the investment be worth 50% more than it was originally and how old will the student be when the investment is worth about 8100.000? (3- Investment is worth 50% more alter 25 years. and the investment is worth $100,000 when the student is about 31 years old. Q Investment is worth 50% more alter 31 years. and the investment is worth $100,000 when the student is about 25 years old. {3: Investment is worth 50% more alter 14 years. and the investment is worth $100,000 when the student is about 31 years old. 0 Investment is worth 50% more alter 5 years, and the investment is worth $100,000 when the student is about 25 years old. The logarithmic function y = logs: + 7.9 can be used to determine the magnitude, y: of an earthquake given an intensity comparison, x: of a previous earthquake, in this case a 19 earthquake. 14 13 12 11 10 9 h 'g 3 7 8' ' 6 E 5 O '15: II a 3 3 2 1 10 12 14 16 13 Intensity comparison, 2: What is the magnitude of an earthquake, y, that is 10 times as intense as this previous earthquake (rounded to the nearest tenth)? What intensity, x, will an aftershock with a magnitude of}: = 8.7 (rounded to the nearest whole number) have when compared to the original 19 earthquake? O Magnitude of earthquake y = 39.0, Intensity comparison x = 4 times. O Magnitude of earthquake y = 9.5, Intensity comparison x = 3 times. O Magnitude of earthquake y = 8.9, Intensity comparision x = 6 times. O Magnitude of earthquake y = 8.9, Intensity comparison x = 2 times.In a recent stock market downturn, the value of a $500 stock is decreasing at 1.2% in a month. This situation can be modeled by the equation A(t) = 500(0.988)12, where A(t) is the final amount and t is time in years. Assuming the trend continues, what is the equivalent annual devaluation rate of this stock (rounded to the nearest tenth of a percent) and what is it worth (rounded to the nearest cent) after 1 year? O 14.4% and $440.00 O 13.5% and $432.57 O 98.8% and $494.00 86.5% and $432.57 A motorcycle is depreciating at 13% per year, every year. A student's $10,900 motorcycle depreciating at this rate can be modelled by the equation V(t) = 10, 900(0.87)*. What is an equivalent equation for this vehicle as a monthly depreciation, and using this equation, what will the motorcycle be worth (rounded to the nearest dollar) 6 years after purchase? 10, 900(0.9885); $10, 169 10, 900(0.9885) 12 ; $4, 740 10, 900(0.8700) 12 ; $4, 727 10, 900(1.13)-; $5, 235The graph of y = 10* + 5 is shown. What is the y-intercept, the horizontal asymptote, and does it represent exponential growth or decay? 18 -16 --14 12 -10 -2 4 O y-int: (0, 5), Horizontal Asymptote is y = 6, and this is exponential growth O y-int: (0, 6), Horizontal Asymptote is x = 1, and this is exponential decay O y-int: (6, 0), Horizontal Asymptote is y = 1, and this is exponential decay O y-int: (0, 6), Horizontal Asymptote is y = 5, and this is exponential growthConsider the graph of the function y = 32(#-3) - 1. LE 8 8 Identify the domain and range of the function. O domain: > > -1; range: all real numbers O domain: all real numbers; range: y > -1 O domain: all real numbers; range: y -2.31 O Horizontal Asymptote: none, Range: y > 2.31 O Horizontal Asymptote: none, Range: y 2.31 The population of a particular town is given by the function P(t) = 920(1.03)#, where t is the time in years and P(t) is the population after + years. What is the current population, the percentage growth rate, and the population size (rounded to the nearest whole person) in 4 years? Hint: Percentage Growth Rate = r x 100, in A = An(1 + r)*. O 920, 6% semiannually, and 1,466 O 920, 6% annually, and 1, 165 O 920, 0.6% per year, and 7,801 O 920, 60% semiannually, and 4,135 After a devastating winter, where thousands of fish died, an environmental scientist has replenished the trout stock in a fishing pond. He started with 5,000 baby trout and has finished a count to find that in 8 years the population is now estimated to be 33,000. Assuming an exponential growth pattern, what is the annual growth rate (rounded to the nearest tenth of a percent) of the new trout fish population? Hint: A(t) = Ao(1 + r), where A(1) is the final amount, Ap is the initial amount, r is the growth rate expressed as a decimal, and t is the time. O 79.0% O 24.4% O 26.6% O 2.7%