The table shows the estimated number of deer living in a forest over a 5 year period. Which type of function best models the data? Write an equation to model the data.
Year/ estimated population
0 | 102
1 | 82
2| 65
3| 52
4 | 42
A. Linear; y=0.8x + 102
B. Quadratic; y=0.8x^2 + 102
C. Exponential; y=102 × 0.8^x
D. Quadratic; y = 102x^2 + 0.8
Based on the given data, the number of deer seems to be decreasing over time. A linear function would not be appropriate since it would predict a constant rate of change, which does not match the data. A quadratic function (option B) would predict a U-shaped curve, which also does not match the decreasing trend in the data.
An exponential function (option C) is the type of function that best models the data since it involves a constant ratio of decrease. The equation to model the data would be:
y = 102 × 0.8^x