Question

A person is trying to quit chewing gum. They decide they will have 64 pieces in week 1, but each week have half as many as the week before. The function f represents the number of pieces of gum they will have in week n. What is a reasonable domain for this function? Explain your reasoning.

Answer 1

Function is missing.

It is;

f(n) = ½⋅f(n − 1) for n ≥ 2

Answer:

Domain for this function is;

n ≥ 1

Step-by-step explanation:

We are told They decide they will have 64 pieces in week 1,

Thus;

f(1) = 64

From the function given;

f(n) = ½⋅f(n − 1)

So;

f(2) = ½•f(2 - 1)

f(2) = ½•f(1)

f(2) = ½ • 64

f(2) = 32

Also;

f(3) = ½•f(3 - 1)

f(3) = ½•f(2)

f(3) = ½ × 32 = 16

Looking at the steps, they follow a general pattern of;

f(n) = 64•½^(n - 1) for n ≥ 1

Thus, the domain for the function for n weeks after the first one is n ≥ 1