To determine the type of function, we need to analyze the relationship between the years (x) and the corresponding values of B(x), M(x), and S(x).
For B(x):
From the given data, we can see that as the years (x) increase, the values of B(x) also increase but not exponentially. The values seem to be increasing linearly, as the values of B(x) are being multiplied by a constant factor of 3 each year (2 * 3 = 6, 6 * 3 = 18, 18 * 3 = 54, and so on). Therefore, B(x) is a linear function.
For M(x):
From the given data, we can see that as the years (x) increase, the values of M(x) also increase but not linearly. The values seem to be increasing at an increasing rate, suggesting a quadratic relationship. To confirm this, we can calculate the ratios of consecutive terms: (120-20)/(6-2) = 100/4 = 25 and (420-120)/(18-6) = 300/12 = 25. Since the ratios are constant, it indicates a quadratic relationship, and therefore, M(x) is a quadratic function.
For S(x):
From the given data, we can see that as the years (x) increase, the values of S(x) increase rapidly. The values seem to be increasing exponentially, as each term is close to being tripled from the previous term (38 * 3 = 114, 81 * 3 = 243, 124 * 3 = 372, and so on). To confirm this, we can calculate the ratios of consecutive terms: 81/38 ≈ 2.13, 124/81 ≈ 1.53, 167/124 ≈ 1.35. Since the ratios are not constant, it indicates an exponential relationship, and therefore, S(x) is an exponential function.
Regarding the white-handed gibbon population:
The given data does not provide any information about the white-handed gibbon population (W(x)). Therefore, we cannot determine its type of function without further information or data.
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.
1 answer