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 picksOption 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 pickedWrite a 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. Option - A Option - 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?Notice that in this assignment Lucy gets more money from linear growth at first. However, while exponential growth starts out slow at first it grows very quickly. Look on line to find at least one other item in life that grows exponentially and provide a short description.Grading rubric that I will use to evaluate this assignment is given below.

Answered: Image /qna-images/answer/7328ed6b-983c-4209-9a2e-388a933f3809.jpg

Answered: Consider Mr. Smith has an apple…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Question

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

Write a linear function to model option A.
Option B can be modeled by an exponential function of the form P_n=0.01(3)^n-1.
Write out the earnings for first couple of bushels for both options A and B.

Option - A Option - 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?
Notice that in this assignment Lucy gets more money from linear growth at first. However, while exponential growth starts out slow at first it grows very quickly. Look on line to find at least one other item in life that grows exponentially and provide a short description.