We appreciate your visit to Types of Functions Scientists are studying the population of a rare species of primates known as Javan gibbons on the Raja Ampat Islands in Indonesia. This page offers clear insights and highlights the essential aspects of the topic. Our goal is to provide a helpful and engaging learning experience. Explore the content and find the answers you need!
Answer :
The first difference is linear with time and pop. growth. The second difference is constant
How to solve
The data presented shows the growth of the Javanese gibbon population on three different islands over time.
Analyze data to determine growth function by plotting and observing curve shape. Since the table only has data, analyze trends by comparing consecutive terms.
To do this, we can calculate the first difference and the second difference in the population data.
The first difference:
- Swing: 40 - 30 = 10, 50 - 40 = 10, 60 - 50 = 10
Example: 60 - 50 = 10, 75 - 60 = 15, 90 - 75 = 15
- Salavati: 80 - 60 = 20, 100 - 80 = 20, 120 - 100 = 20
The second difference:
- Batanta: 10 - 10 = 0, 10 - 10 = 0
- Example: 15 - 10 = 5, 15 - 15 = 0
- Salavati: 20 - 20 = 0, 20 - 20 = 0
The first difference is linear with time and pop. growth. The second difference is constant. The population growth model is a linear function:
M(x) = mx + b
where x is the time in years, m is the slope (population growth rate), and b is the y-intercept (initial population).
Read more about linear function here:
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The Complete Question
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.
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.
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