Question

A towns population has been growing literally

Answer 1

$\bf \begin{array}{ccll} \stackrel{\textit{years since 2000}}{t}&\stackrel{population}{p}\\ \text{\textemdash\textemdash\textemdash}&\text{\textemdash\textemdash\textemdash}\\ 2&29400\\ 5&36000 \end{array}\\\\ -------------------------------\\\\ \begin{array}{lllll} &x_1&y_1&x_2&y_2\\ % (a,b) &({{ 2}}\quad ,&{{ 29400}})\quad % (c,d) &({{ 5}}\quad ,&{{ 36000}}) \end{array}$

$\bf slope = {{ m}}= \cfrac{rise}{run} \implies \cfrac{{{ y_2}}-{{ y_1}}}{{{ x_2}}-{{ x_1}}}\implies \cfrac{36000-29400}{5-2}\implies \cfrac{6600}{3} \\\\\\ 2200 \\\\\\ % point-slope intercept \stackrel{\textit{point-slope form}}{y-{{ y_1}}={{ m}}(x-{{ x_1}})}\implies \stackrel{y}{p}-29400=2200(\stackrel{x}{t}-2) \\\\\\ p-29400=2200t-4400\implies p(t)=2200t+27200$

how many in 2007?  well, 2007 is 7 years after 2000, thus set t = 7,to get p(t).