Consider Mr. Smith has an apple orchard. He hires his daughter, Lucy, to pick apples and offers her two payment options:

Option A:  $1.50 for each bushel of apples she picks

Option B:  1¢ cent for picking one bushel, 3¢ cents for picking two bushels, 9¢ cents for picking three bushels, and so on, with the amount of money tripling for each additional bushel picked. On a separate paper, answer the following questions. Show all your work. Answers and work need to be written clearly

Create linear function to model option A.

Option B can be modeled by an exponential function of the form Pn=0.01(3)n-1.  

Write out the earnings for first couple of bushels for both options A and B.

Create linear function to model option A.

Option B can be modeled by an exponential function of the form Pn=0.01(3)n-1.  

Write out the earnings for first couple of bushels for both options A and B. If Lucy picks six bushels of apples, which option should she choose? 

If Lucy picks 12 bushels of apples, which option should she choose? How many bushels of apples does Lucy need go pick to make Option B better than Option A?

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