Question

Let f(x) represent the weight of the jar when there are x marbles, where f(0)=10. Which equation correctly represents f(x) in terms of f(x−1) for all x>0?

A
f(x)=3⋅f(x−1)

B
f(x)=f(x−1)+3

C
f(x)=f(x−1)+3x

D
f(x)=f(x−1)+2x+1

Answer 1

B

Explanation:

f(x)=f(x-1)+3x

Answer 2

B

Explanation:

We essentially have the sequence:

10, 13, 16, 19, 22,25...

This is an arithmetic sequence because each subsequent term differs only by a constant.

And this constant, the common difference, is +3 since each subsequent term is 3 more than the previous term.

Hence, we can write a recursive formula for our sequence.

We will first define our first term. The first term, at x=0, is 10. Hence:

`f(0)=10`

Each term, x, is +3 the previous term (x-1). Therefore:

`f(x)=f(x-1)+3`

Hence, our answer is B.