c.
As found in part (a), the data in the table can be represented by the linear model as follows,
[tex]f(x)=2.928x+270.641[/tex]
Here, 'x' is the number of years after year 2000.
To find: The population in 2080 as predicted by the model.
The value of 'x' corresponding to the year 2080 can be obtained as follows,
[tex]\begin{gathered} x=2080-2000 \\ x=80 \end{gathered}[/tex]
Substitute the value of 'x' in the model for population,
[tex]\begin{gathered} f(80)=2.928\cdot(80)+270.641 \\ f(80)=234.24+270.641 \\ f(80)=504.881 \\ f(80)\approx504.9 \end{gathered}[/tex]
Thus, the population in 2080 will be 504.9 million approximately, as predicted by the linear model.
