Types of Functions
Scientists are studying the population of a rare species of primates, known as a Javan gibbons, on the Raja Ampat Islands in Indonesia. They are studying the gibbons on three different islands, Batanta, Misool, and Salawati. The scientists studied the population growth and recorded the data in the table.

Years (x) Batana
B(x) Misool
M(x) Salawati
S(x)
0 2 20 38
1 6 120 81
2 18 420 124
3 54 920 167
4 162 1620 210
5 486 2520 253
What type of function is B(x), linear, quadratic or exponential? Justify your answer and show calculations to support your conclusion.
What type of function is M(x)? Justify your answer and show calculations to support your conclusion.
What type of function is S(x)? Justify your answer and show calculations to support your conclusion.
A white-handed gibbon population, represented by W(x), was recorded at a fourth location, starting in year three.
The graph shows the function w(x), which includes five points. The points are located at (3, 24), (4, 48), (5, 96), (7, 384), (8, 768), and (9, 1536).
Of the functions B(x), M(x), and S(x), which function is the same type as W(x)? Justify your answer and show calculations to support your conclusion