Question

Which kind of function best models this relationship?
Time (years) Branches
\[0\]
\[16\]
\[2\]
\[23\]
\[4\]
\[33\]
\[6\]
\[48\]
\[8\]
\[69\]
\[10\]
\[99\]
Choose 1 answer:
Choose 1 answer:
(Choice A) Linear
A
Linear
(Choice B) Exponential
B
Exponential

Answer 1

To determine which kind of function best models the relationship between time (in years) and the number of branches, we can analyze the data provided.

The table shows:
- At year 0, there are 16 branches.
- At year 2, there are 23 branches (an increase of 7 branches).
- At year 4, there are 33 branches (an increase of 10 branches).
- At year 6, there are 48 branches (an increase of 15 branches).
- At year 8, there are 69 branches (an increase of 21 branches).
- At year 10, there are 99 branches (an increase of 30 branches).

It appears that the number of branches is increasing at a non-constant rate, which suggests that the relationship might be exponential rather than linear. In a linear function, the increases would be constant, whereas here the increases are growing.

Based on this observation, the best fit for this data is likely to be:

(Choice B) Exponential

So, the answer is:
B Exponential