\(\displaystyle First \ of \ all, \ populations \ don't \ grow \ linearly, \ they \ grow \ exponentially.\)
\(\displaystyle Man \ will \ always \ produced \ faster \ than \ the \ land \ he \ occupies \ can \ sustain \ him, \ hence\)
\(\displaystyle a \ land \ grab \ (known \ as \ war) \ is \ in \ order. \ Thomas \ Malthus.\)
\(\displaystyle Hence, \ the \ usual \ exponential \ growth \ model \ is \ P(t) \ = \ Ce^{kt}.\)
\(\displaystyle Therefore, \ for \ the \ data \ given, \ we \ have: \ P(t) \ = \ 7000e^{.2t}.\)
\(\displaystyle Note, \ if \ we \ put \ the \ data \ given \ into \ a \ linear \ function, \ then \ we \ get:\)
\(\displaystyle P(t) \ = \ .2t+7000 \ which \ doesn't \ make \ any \ sense \ (assuming \ t \ is \ in \ years).\)
