Using a graphing calculator, we obtain the following regression model.
Thus, the regression model is:
[tex]\begin{gathered} P(t)=0.261212t+37.4545 \\ P(t)=0.26t+37.45 \end{gathered}[/tex]For part b, find the value of x by subtracting 2025 by 2010. Thus, the value of t is 15. Substitute 15 for t in the obtained equation in part a and then solve for P(t).
[tex]\begin{gathered} P(t)=0.26t+37.45 \\ =0.26(15)+37.45 \\ =3.9+37.45 \\ =41.35 \end{gathered}[/tex]Thus, there is approximately 41.4 million people on 2025.
For part c, substitute 40 for P(t) in the obtained equation in part a and then solve for t.
[tex]\begin{gathered} P(t)=0.26t+37.45 \\ 40=0.26t+37.45 \\ 40-37.45=0.26t \\ 2.55=0.26t \\ t=\frac{2.55}{0.26} \\ t\approx9.807692308 \\ t\approx10 \end{gathered}[/tex]Add the obtained value of t to 2010. Thus, the population will reach 40 million in 2020.
