The fox population in a certain region has a continuous growth rate of $4$ percent per year. It is estimated that the population in the year $2000$ was $16400.$

$($a$)$ Find a function that models the population $t$ years after for $2000).$

Your answer is $P(t)=$

$($b$)$ Use the function from part $($a$)$ to estimate the fox population in the year $2008.$

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

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