Question

(a) find a linear function that models the data, with x equal to the number of years after 2000 and f(x) equal to the population in millions. f(x)=2.857x + 274.864 (type integers or decimals rounded to three decimal places as needed.) (b) find f(65). state what the value of f(65) means. f(65)= (round to one decimal place as needed.)

Explanation:

Step1: Substitute x = 65 into the function

Given \(f(x)=2.857x + 274.864\), substitute \(x = 65\). So \(f(65)=2.857\times65+274.864\).

Step2: Calculate the product

\(2.857\times65 = 185.705\). Then \(f(65)=185.705 + 274.864\).

Step3: Calculate the sum

\(185.705+274.864 = 460.569\). Rounding to three - decimal places, it is \(460.569\). Rounding to one - decimal place, \(f(65)\approx460.6\).

Answer:

(a) The linear function is \(f(x)=2.857x + 274.864\).
(b) \(f(65)=460.6\). It means that the population (in millions) 65 years after 2000 is approximately 460.6 million.