Step 1
To solve the problem, we need to integrate the given expression and evaluate using the given time.
[tex]\int_0^3\frac{\sqrt{t}}{15}dt[/tex][tex]\int_0^3\frac{1}{15}(t)^{\frac{1}{2}}dt[/tex][tex]=\frac{1}{15}(\int_0^3(t)^{\frac{1}{2}})dt[/tex][tex]\begin{gathered} Apply\text{ the power rule} \\ =\frac{1}{15}\left[\frac{2}{3}t^{\frac{3}{2}}\right]^3_0 \\ Compute\text{ the boundaries} \\ =\frac{1}{15}\left[\frac{2}{3}(3)^{\frac{3}{2}}\right]_^-\frac{1}{15}\left[\frac{2}{3}(0)^{\frac{3}{2}}\right]_^ \\ =\frac{1}{15}(\frac{2}{3}(3)(\:3^{\frac{1}{2}}))-0 \end{gathered}[/tex][tex]\begin{gathered} =\frac{2}{15}(\sqrt{3}) \\ =\frac{2\sqrt{3}}{15} \\ \end{gathered}[/tex][tex]\begin{gathered} \int_0^3\frac{\sqrt{t}}{15}dt=\frac{2\sqrt{3}}{15}=0.2309401077 \\ \int_0^3\frac{\sqrt{t}}{15}dt=0.231 \end{gathered}[/tex]
Answer; The amount dumped after 3 days is
[tex]0.231[/tex]
