A small company of science writers found that its rate of profit $($in thousands of dollars$)$ after t years of operation is given by $P^{\text{'}}(t)=(7t+14)(t^2+4t+3{)}^{\frac{1}{5}}.$

$($a$)$ Find the total profit in the first three years.

$($b$)$ Find the profit in the fourth year of operation.

$($c$)$ What is happening to the annual profit over the long run?

$($a$)$ The total profit in the first three years is $

$($Round to the nearest dollar as needed.$)$