Andrew and Charles were each asked to find the value of
when x = 10. Their work is shown below. Homework Help ✎
Andrew: “When I tried other values of x for a different problem, I found that
, , and . So, I predict that must equal 10.”
Charles: “Since (xa)b = xab, then
must equal . I can simplify this to become . Therefore must be x and when x = 10, .”
Who used inductive reasoning? Who used deductive reasoning? For each person, explain how you know.
What is the difference between inductive and deductive reasoning?
Without a calculator, find the value of
when x = 312 and when x = 7344.
Andrew used inductive reasoning because he extended a pattern; Charles used deductive reasoning because he based his reasoning on properties of exponents.
What are the definitions of inductive and deductive?
Follow the reasoning of Andrew and Charles.