The fox population in a certain region has a continuous growth rate of $7$ percent per year. It is estimated that the population in the year $2010$ was $18700.$

$($a$)$ Find a function that models the podulation $t$ vears after $2010(t=0$ for $2010).$

Your answer is $P(t)=$

$($b$)$ Use the function from part $($a$)$ to estimate the fox population in the year $2015.$

Your answer is $($the answer must be an integer$)$