1. (5 pts) Which of these graphs represent a one-to-one function? 2. (5 pts) Convert to a logarithmic equation: 7 = 2401. 2. ______ A. B. C. D. 3. (10 pts) Based on data about the growth of a variety of ornamental cherry trees, the following logarithmic model about these trees was determined: where = age of tree in years and ( ) = height of tree, in feet. Using the model, (a) At age 3 years, how tall is this type of ornamental cherry tree, to the nearest tenth of a foot? (b) At age 12 years, how tall is this type of ornamental cherry tree, to the nearest tenth of a foot? 4. Solve the equation. all proposed solutions. 5. (10 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 – – 10 and ( ) = 3 + 1 (a) Find the composite function and simplify the results. Show work. (b) Find . Show work. 8. (15 pts) Let A. Shift the graph of to the left by 1 unit and up by 4 units. B. Shift the graph of to the right by 1 unit and up by 4 units. C. Reflect the graph of across the -axis and shift up by 4 units. D. Reflect the grap
h of across the -axis and shift up by 4 units. = 0.3476 + 10.948 6.0778 where = Time of day (hour) and = Temperature (in degrees) (b) Use the quadratic polynomial to estimate the outdoor temperature at 7:30 am, to the nearest tenth of a degree. (work optional) = 0.3476 + 10.948 6.0778 75 = 0.3476 + 10.948 6.0778 10. (10 pts) 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 25 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: When 25 minutes have elapsed, the estimated coffee temperature is ________ degrees. (c)Suppose the coffee temperature is 100 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).