The table shows the estimated number of deer living in a forest over a five-year period. Are the data best represented by a linear, exponential, or quadratic model? Write an equation to model the data.
This is the table :
Year Estimated Population
0 102
1 82
2 65
3 52
4 42
A. Quadratic; y=0.8x^2+102
B. Exponential; y=102 x 0.8^x
C. Quadratic; y =102x^2 +0.8x
D. Linear; y=0.8x+102
Since the population of deer decreases over time, the data is not best represented by an exponential model.
Looking at the data, it can be observed that the population follows a decreasing trend, suggesting a quadratic or linear relationship.
To determine if the data is best represented by a linear or quadratic model, let's examine the differences between consecutive population values:
Year 0 to 1: -20
Year 1 to 2: -17
Year 2 to 3: -13
Year 3 to 4: -10
The differences between consecutive values are not consistent, indicating that the data is not best represented by a linear model.
Therefore, the data is best represented by a quadratic model.
From the table, the equation to model the data is:
y = 0.8x^2 + 102
So, the correct answer is A. Quadratic; y=0.8x^2+102.