Answer:
f(x) ≈ 58.20x2 + 18.96x + 34.46
Explanation:
Notice that the year data are evenly spaced. Check the first differences between the total number or units to see if the data set is linear.
First Differences
113 − 34 = 79
304 − 113 = 191
615 − 304 = 311
1042 − 615 = 427
1584 − 1042 = 542
Because the first differences are not constant, a linear model is not the best model of the data. Check the second differences to see if the data set can be modeled by a quadratic function.
Second Differences
191 − 79 = 112
311 − 191 = 120
427 − 311 = 116
542 − 427 = 115
The second differences are approximately the same so we will use a quadratic function to represent the data.
Enter the data into a calculator. Plot the data and find the quadratic regression equation that best models the data.
f(x) ≈ 58.20x2 + 18.96x + 34.46