The parent function for each graph below is of the form y = a b x . y equals , eh b to the x , .  Write the parent function. Then write a function for the translation indicated.

38. 

    translation: left 4 units, up 3 units

39. 

    translation: right 8 units, up 2 units

40. 

    translation: right 6 units, down 7 units

41. 

    translation: left 15 units, down 1 unit

42. Physics At a constant temperature, the atmospheric pressure p in pascals is given by the formula p = 101.3 e − 0.001 h , p equals . 101.3 , e super negative , 0.001 , h end super . comma  where h is the altitude in meters. What is p at an altitude of 500 m?

C Challenge

43. Psychology Psychologists use an exponential model of the learning process, f ( t ) = c ( 1 − e − k t ) , f open t close equals c open 1 minus . e super negative k t end super . close comma  where c is the total number of tasks to be learned, k is the rate of learning, t is time, and f (t) is the number of tasks learned.
    1. Suppose you move to a new school, and you want to learn the names of 25 classmates in your homeroom. If your learning rate for new tasks is 20% per day, how many complete names will you know after 2 days? After 8 days?
    2. Graphing Calculator Graph the function on your graphing calculator. How many days will it take to learn everyone's name? Explain.
    3. Open-Ended Does this function seem to describe your own learning rate? If not, how could you adapt it to reflect your learning rate?

44. Landscaping A homeowner is planting hedges and begins to dig a 3-ft-deep trench around the perimeter of his property. After the first weekend, the homeowner recruits a friend to help. After every succeeding weekend, each digger recruits another friend. One person can dig 405  ft  3 405 , ft cubed of dirt per weekend. The figure below shows the dimensions of the property and the width of the trench.

    

    1. Geometry Determine the volume of dirt that must be removed for the trench.
    2. Write an exponential function to model the volume of dirt remaining to be shoveled after x weekends. Then, use the model to determine how many weekends it will take to complete the trench.

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