PC - Exponential and Logarithmic Functions
#1 Give the end behavior limits for y = -2(3)^x.
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#10 Find the percent of increase/decrease for y = 3(1.2)^x.
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#11 Find the percent of increase/decrease for y = 2(.85)^x.
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#12 Find the percent of increase/decrease for y = (2)^x.
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#13 Find the percent of increase/decrease for y = 4(5.2)^X.
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#14 Find the percent of increase/decrease for y = 8(.98)^x.
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#15 Write an exponential function to model an initial amount of 9.2 that increases 20% per year.
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#16 Write an exponential function to model an initial amount of 3 that increases 12% per year.
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#17 Write an exponential function to model an initial amount of 6.3 that decreases 16% per year.
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#18 Write an exponential function to model an initial amount of 1.6 that decreases 0.5% per year.
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#19 Write an exponential function to model an initial amount of 4 that decreases 10% every 5 years.
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#2 Give the end behavior limits for y = -3(¾)^x.
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#20 Graph y = 2(1/2)^x.
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#21 Graph y = -2(2)^x.
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#3 Give the end behavior limits for y = 4(2)^x.
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#30 Write the formula for the inverse of: f(x) = 2(4)^x
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#31 Write the formula for the inverse of: f(x) = 3^(x-2)
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#32 Write the formula for the inverse of: f(x) = 2^x + 3
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#33 Write the formula for the inverse of: f(x) = log₃(x) - 2
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#34 Write the formula for the inverse of: f(x) = log₄(x+1) - 3
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#35 Graph y = 2log(x-1).
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#36 Graph y = -log(x) + 3.
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#37 Graph y = log₃(x+2) - 1.
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#38 Graph y = log₂(x+3) + 1.
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#4 Give the end behavior limits for y = -¼(½)^x.
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#42 Write as a single log term: lnx² - 3ln(xy)
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#43 Write as a single log term: 2logx + 3log y
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#44 Write as a single log term: 5logx + log(xy)
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#45 Write as a single log term: 3log₂x - 2log₂x
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#46 Expand to a sum or difference of logs: log(x³/y⁴)
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#47 Expand to a sum or difference of logs: ln(x²y³)
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#48 Expand to a sum or difference of logs: log₂((x²y⁴)/m³))
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#49 Evaluate, rounding to the nearest thousandth: log₃4
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#5 Give the end behavior limits for y = 4(0.3)^x.
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#50 Evaluate, rounding to the nearest thousandth: log₅200
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#51 Evaluate, rounding to the nearest thousandth: log₆42
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#52 Solve, rounding to the nearest thousandth, if necessary: 7 + 2log(5x) = 11
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#53 Solve, rounding to the nearest thousandth, if necessary: log(x-16) = 2 - log(x-1)
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#54 Solve, rounding to the nearest thousandth, if necessary: log(x+3) = log(3x+1)
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#55 Solve, rounding to the nearest thousandth, if necessary: log₂x = 5
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#56 Solve, rounding to the nearest thousandth, if necessary: 4^(x+3) = 2^(5x+1)
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#57 Solve, rounding to the nearest thousandth, if necessary: 6^x = 3
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#58 Solve, rounding to the nearest thousandth, if necessary: 2^x = 15
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#59 Solve, rounding to the nearest thousandth, if necessary: 2^(x-1) = 3^(x+4)
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#6 Give the end-behavior limits for y = -3(4)^x.
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#60 In 1985, there were 285 cell phone subscribers in a town. The number of subscribers increased by 75% per year after 1985. How many subscribers were there in 1994?
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#61 Each year a school sponsors a tennis tournament. Play starts with 128 participants. During each round, half the players are eliminated. How many players remain after 5 rounds?
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#62 You buy a new computer for $2100. The computer's value decreases by 45% each year. When will the computer's value be $600?
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#63 You drink a beverage with 120 mg of caffeine. Each hour, the caffeine in your system decreases by about 12%. How long until you have 10 mg of caffeine?
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#64 Write an exponential model for this data: x y 0 2 1 7 2 24.5
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#7 Give the domain and range for y = -2(6)^x.
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#8 Give the domain and range for y = 4(0.3)^x.
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#9 Give the domain and range for y = 4(2)^x.
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#25 Describe the transformations from y=3^x. y=-(3)^x
reflect over the x-axis
#27 Describe the transformations from y=log₃x. y=-4 log₃x
reflect over the x-axis, stretch vertically by factor 4
#41 Describe the transformation(s) from y=log₅x for y=-½log₅(3x).
shrink horizontally by factor 1/3, reflect over the x-axis, and shrink vertically by factor 1/2
#23 Describe the transformations from y=3^x. y=¾(3)^x + 1
shrink vertically by factor 3/4, and translate 1 unit up
#22 Describe the transformations from y=3^x. y=2(3)^x
stretch vertically by factor 2
#40 Describe the transformation(s) from y=log₅x for y=3log₅(x).
stretch vertically by factor 3
#24 Describe the transformations from y=3^x. y=(3)^(x-1)
translate 1 unit right
#26 Describe the transformations from y=log₃x. y = log₃x - 2
translate 2 units down
#39 Describe the transformation(s) from y=log₅x for y=log₅(x) + 2.
translate 2 units up
#28 Describe the transformations from y=log₃x. y=log₃(x+5)
translate 5 units left
#29 Describe the transformations from y=log₃x. y=log₃(x-8)
translate 8 units right