Lesson 21 SummarySuppose that the input-output pairs of a bivariate dataset have the following property: for every two inputs that are a given difference apart, the difference in their corresponding outputs is constant. Then an appropriate model for that dataset could be a linear function.
For each table in Problems 1–6, classify the data as describing a linear relationship, an exponential growth relationship, an exponential decay relationship, or neither. If the relationship is linear, calculate the constant rate of change (slope), and write a formula for the linear function that models the data. If the function is exponential, calculate the common quotient for input values that are distance 1 apart, and write the formula for the exponential function that models the data. For each linear or exponential function found, graph the equation y = f(x).
Here is a classic riddle: Mr. Smith has an apple orchard. He hires his daughter, Lucy, to pick apples and offers her two payment options.
Option A: per bushel of apples picked.
Option B: cent for picking one bushel, cents for picking two bushels, cents for picking three bushels, and so on, with the amount of money tripling for each additional bushel picked.
a. Write a function to model each option.
b. If Lucy picks six bushels of apples, which option should she choose?
c. If Lucy picks bushels of apples, which option should she choose?
d. How many bushels of apples does Lucy need to pick to make option B better for her than option A?
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