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1. Oscar is driving for a taxi company where he earns a base pay of $250 per week and a 7% commission on the charges he collects from his customers per week. Write an expression to represent Oscar's profit, P, each week when he collects d dollars from his customers. O P = 250d + 7 O P= 7d+ 250 O P= 0.07+ 250d O P= 0.07d+ 2502. At what point does the exponential function overtake the linear function on the interval (0,co)? [Type your answer as an ordered pair with no spaces.] Ax) = 2x g(x) = 2*Q4. Consider the function A(x) = (3)* to answer the following questions. Part A - From just looking at the equation of the function, would you expect the average rate of change for this function to be positive or negative? Explain your reasoning. Part B - Find the average rate of change on the interval [0, 2]. Show all of your work.5. Which of these is not like the other? Explain. Option 1: {(1,2), (2,4), (3,8), (4, 16), (5,32)} Option 2: y = 4(1.6)' Option 3: 4x - 2= * - 3y 4+ 2 - -5 - 4 -3 2 -1 14 2 3 -2 -3 -4 Option 4: O Option 2 because it has a variable in the exponent where as the equations modeling the rest of the options do not. O Option 1 because it is a continuous function where as the rest of the functions are discrete. O Opton 3 because it is neither linear or exponential where as the rest of the options are either linear or exponential. O Option 3 because it is a linear function where as the other options are exponential functions.1. What value of x satisfies the following equation? 25* = 125*+3 (Only type your numerical answer in the answer box.)2. Rewrite the following expression with only x in the exponent: 64 O 32 O O O 32*4. Which of the following equations has the same solution as = g*-17 4(x - 3) = O N4X = 9 O 2 x- 2 3 O5. The trend in iPhones over the past decade shows that the average iPhone depreciates by 53% per year. This can be modeled by the equation (!) = V. (1- 0.53)' where t is in years. Manipulate this equation so that it models the value of the average iPhone after w weeks. O VW) & V. (0.009) " O V( W) * V. (8.89) " O V(W) = V. (0.9856) " O WW) NV. (0.47) "1. Which of the following has the greatest y-intercept? O Y = - + 2 O y= 3(-5) _4 O Y = 3 (*+5) O Y = + 42. Tori is attempting to sketch the graph of the function /(x) = 3"* + 1 without using a graphing calculator. Which of the following is an asymptote of the graph? O x= 2 O x=1 O y= 2 O y=1Q3. The half-life of a particular drug is 6 hours. When given an adult dosage, the following function can be used to model the amount of drugs, d, in an adult's system over time t in hours: al" A() = 50(0.5) What would be a suitable domain and range to view only the important features of this graph? Explain your reasoning.4. Which of the following is NOT an exponential function? O h(x) = 14 O 3x g(x) = NI O Ax) = (-5)*-1 O m(x) = 6*W Q 5. The graph of A(x) = ab" is shown below: 5 3+ 2+ 1 2 3 4 -2 Which statement is TRUE about f (x)? O There is a y-intercept at (0, -1). There is an asymptote at y = 0 O The range is all real numbers. O The domain consists of all x-values greater than -1.(0.33): 1. Using a calculator, evaluate A(t ) = 8e for t = 2 O 22.255 O 15.478 O 1435.253 O 14.353Q 2. Which of the following is/are an example(s) of exponential growth? Select all examples. wi A(t) = 560e A(t) = 560e" A(t) = 560 A(t) = 560eQ 4. Which of the following functions represents discrete exponential decay? O 03 (1) A(t ) = 27 1+ .03 12 O A(t ) = 27e 03 (1) O .03 (1) A(t) = 27 1-.03 12 O A(t) = 27e -0.03 (1)5. Hinata researched rabbit population in the area and created the following model to assist her in predicting how many rabbits would exist at t = 12, A(12) = 80e 0.04(12] . What value represents the growth rate of rabbits in her model? O e O 80 O 12 O 0.046. A radioactive substance has a decay rate of 15% per year. If we initially have 7 grams, which of the following models will find the how many grams will remain in t years. O A(t) = 7e-0.15: O A(t ) = 70 15 O A(t) = 7 15 O A(t) = 7e-15t1200 Q8. Using a calculator, evaluate A(( ) = for t = 5 (0.3) (1) e Toggle bookmark O 662.183 O 267.756 5378.027 4444.9096. Solve for x. Round to four decimal places if necessary. 1.8 = 2.7 O x=-0.2959 O x=-3.3796 O x=-1.1836 O *=-0.84498. Solve for *, showing all steps. Round your answer to four decimal places. 0.232 = 5.7Q9. Use the change of base rule to solve. Show all steps. log, (0.25) = x5. Solve for *, rounding to the nearest integer if necessary. Fully justify your response by showing all algebraic steps. log, (8) = log, (2)7. Change from logarithmic form to exponential form y = ab". log, = X O y= 2. 7* O y= 7. 2" y= 4(2) O y ( 7 ) *Q9. Change from exponential form to logarithmic form. g = b(n) O log, (ng ) =f O 10g. O O log, (bg ) =fm[ll) 4. State the value of e O 11' Oe O 11 O ell6. Use the laws of logarithms to rewrite log, + log (40) - log, (2) as a single logarithm. O log, (16) O log (32) O log (128) O log, (64)8. Simplify log. (x) + log. O log, [ x - y O log, ( x - y ) O log, ( x + y ) log, (xy )W Q 9. log, ( a' - 1 ) - log, (a+ 1) is equivalent to O log, (a - 1) O log, (a' +a' -a-1) O log, (a + a) O log, (a - a-2Q 1. Select the inverse of f(x) - (5) * - 1. Of (x) = log, (4x + 4) Of ( x ) = 5* -1 O f (x) = 10g, x-1 Of (x) = log, (4x -4)2. Select the function that matches the table of values. X y -3 23 -2 13 4 -1 2 7 3 -5 O Ax ) = (-2) *+3 O Ax) = log, (-2) +3 O Ax) = (-2)"+3 O Ax) = log, (x) +3Q 3. Select the range of f(x) = log(x + 7). O y20 O All real numbers O y >-7 Oy>0Q4. Select the value of a such that alog, (x) is equivalent to log, (x). O a = 4 O a= 3 O a=4 O a= 12x- 2 Q 5. Select the inverse of g(x) = log 5 O g" (x) = 2(10)* +5 O g- (x) = 5(10)* +2 O gil ( x) = 5(2)" O g-(x) = 10(5) +26. Select the description of the transformation from f( x) = log, (x) to g(x) = log (x). O Vertical stretch by a factor of 3. O Vertical stretch by a factor of O Vertical stretch by a factor of 2. O Horizontal stretch by a factor of 2.8. Describe how the graph of y = log 1 relates to the graph of y = log(x).Q9. If log3(*) = 17, what is the value of log 1/3 ()? O 317 O 1017 O 1 17 O -1710. Select the domain of f( x ) = In(x + 7). O O xzer>e O O