Answer:
3) y = 1.209x² + 12.999x + 504.257
4) 4,177,000
Step-by-step explanation:
To find the best-fitting quadratic model for the given data, input the data into a quadratic regression tool or statistical calculator.
After entering the data into a statistical calculator we get:
- a = 1.209285714...
- b = 12.998571428...
- c = 504.257142857...
Substitute the found values of a, b and c into the quadratic regression formula, y = ax² + bx + c, rounding each coefficient to 3 decimal places:
[tex]y=1.209x^2 + 12.999x + 504.257[/tex]
To estimate the population in 2020, substitute x = 50 into the model (as 2020 is 50 years after 1970):
[tex]y=1.209(50)^2 + 12.999(50) + 504.257[/tex]
[tex]y=1.209(2500) + 12.999(50) + 504.257[/tex]
[tex]y=3022.5 + 649.95 + 504.257[/tex]
[tex]y=4176.707[/tex]
[tex]y=4177[/tex]
Therefore, the estimated population in 2020 is 4,177 thousand, which is equal to 4,177,000.
