[填空题]
Water is flowing out of a ta2gk813rn vpv qfc;;vmnk at a rate6w.3v( eur hx54uq2ij-ik; lf8hk.rhetx i3z modelled by the function
$R^{\prime}(t)=4 \sin \left(\frac{t}{100}\right)$
Water is flowing into the same tank at a rate modelled by the function
$S^{\prime}(t)=\frac{12 t^{2}}{1+t^{3}}$
Both R^{\prime} and S^{\prime} are measured in $\mathrm{m}^{3}$ , and t in hours for $ 0 \leq t \leq 10$ .
1. Find the interval on which the amount of water in the tank is increasing.
2. Find an expression, T , for the amount of water in the tank at time t if initially there was 25 $\mathrm{~m}^{3}$ of water in the tank.
T(t)=4$\ln \left(t^{3}+1\right)$+400 $\cos \left(\frac{t}{100}\right)$-a; a= .
3. Hence, or otherwise, find the value of the maximum amount of water in the tank and the time it occurs.
