Answer
\[In\,year\,\,\,2030\,population\,\,will\,be\,\,860\]
Work Step by Step
\[\begin{gathered}
General\,form\,of\,linear\,function\,is\, \hfill \\
\, \hfill \\
y = mx + b \hfill \\
\hfill \\
or \hfill \\
\hfill \\
p\,\left( t \right) = mt + l \hfill \\
\hfill \\
we\,\,\,want\,\,growing\,\,rate\,of\,24\,people\,\,per\,year \hfill \\
so\,slope\,of\,the\,function\,\,is\,\, \hfill \\
\hfill \\
m = 24 \hfill \\
\hfill \\
population\,in\,year\,2015\,was\,500\,,\,so\,\,we\,\,\,want\,\,p\,\left( 0 \right) = 500 \hfill \\
because\,t = 0\,\,represents\,yars\,2015.{\text{ }}use\,\,\,this\,information\,to\,find\,l \hfill \\
\hfill \\
500 = 24t + l \hfill \\
\hfill \\
substitute\,\,\,t = 0 \hfill \\
\hfill \\
500 = 24 \cdot 0 + l \hfill \\
\hfill \\
therefore \hfill \\
\hfill \\
l = 500 \hfill \\
\hfill \\
then,\,function\,that\,models\,\,population\,is \hfill \\
\hfill \\
p\,\left( t \right) = 24t + 500 \hfill \\
\hfill \\
year\,\,\,2030\,is\,represented\,\,with\,t = 15\,,\,so\,prediction\,is: \hfill \\
\hfill \\
p\,\left( {15} \right) = 24 \cdot 15 + 500 = 860 \hfill \\
\hfill \\
the\,\,solution\,\,\,is \hfill \\
\hfill \\
p\,\left( t \right) = 24t + 500 \hfill \\
\hfill \\
In\,year\,\,\,2030\,population\,will\,be\,\,860 \hfill \\
\hfill \\
\end{gathered} \]
