Pollution from a factory

antering a lake. The at time $t_z$ is given by $p^{\text{'}}(t)=200t^{\frac{3}{2}},$ where $t$ is the number of years since the factory started introducing elolutants into the lake. lake can accedt a total level of pollution of $4850$ unirs before all fish life in the lake ends. Can the factory operate for $3$ years without killing all the fish in the lake?

Set up definite integral

${\displaystyle \underset{}{\overset{}{}}}dt$

can the factory operate for $3$ years without killing fish in lake