1. (4 pts) Which of these graphs represent a one-to-one function? 2. (6 pts) Based on data about U.S. households, the following logarithmic model was determined: where = year and ( ) = number of U.S. households with cable television, in millions of households. Using the model, (a) How many U.S. households had cable television in the year 1999, to the nearest million? (b) How many U.S. households had cable television in the year 2010, to the nearest million? 3. (4 pts) Convert to a logarithmic equation: 8 = 4096. 2. ___ 4. Solve the equation. all proposed solutions. 5. (8 pts) (a) _______ (fill in the blank) (b) Let State the exponential form of the equation. (c) Determine the numerical value of , in simplest form. Work optional. 6. (10 pts) Let ( ) = 2 5 4 and ( ) = 3 + 1 (a) Find the composite function and simplify the results. Show work. (b) Find . Show work. . (2) (2) 8. (18 pts) Let A. Shrink the graph of horizontally by a factor of 2 and shift up by 3 units. B. Reflect the graph of across the -axis and shift up by 1 unit. C. Shift the graph of to the left by 2 units and up by 3 units. D. Shift the graph of to the right by 2 units and up by 3 units. = 0.3476 + 9.5579 + 4.4284 where = Time of day (hour) and = Temperature (in degrees) (b) Use the quadratic polynomial to estimate the outdoor temperature at 6:30 am, to the nearest tenth of a degree. (work optional) = 0.3476 + 9.5579 + 4.4284 65 = 0.3476 + 9.5579 + 4.4284 10. (10 pts) + (part (e) extra credit at the end) EXPONENTIAL REGRESSION A cup of hot coffee was placed in a room maintained at a constant temperature of 69 degrees, and the coffee temperature was recorded periodically, in Table 1. where = Time Elapsed (minutes) and = Temperature Difference (in degrees) (a) Use the exponential function to estimate the temperature difference when 15 minutes have elapsed. Report your estimated temperature difference to the nearest tenth of a degree. (b) Since = 69, we have coffee temperature = + 69. Take your difference estimate from part (a) and add 69 degrees. Interpret the result by filling in the blank: (c)Suppose the coffee temperature is 105 degrees.Then = 69 = degrees is the temperature between the coffee and room temperatures. (d) Consider the equation = 89.976 where the is filled in with your answer from part (c). Show algebraic work to solve the part (d) equation for , to the nearest tenth. Interpret your results clearly in the context of the coffee application.
