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?

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)   LetState 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 graph 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 REGRESSIONA 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).