Answer
a) $7.09306$
b) $0.75992$ $kg$
Work Step by Step
a)
$\frac{dm}{dt}$ = $CM^{\frac{3}{4}}$
$6$ = $C(100)^{\frac{3}{4}}$
$C$ = $\frac{3\sqrt {10}}{50}$
$\frac{dm}{dt}$ = $\frac{3\sqrt {10}}{50}M^{\frac{3}{4}}$
$\frac{dm}{dt}|_{M=125}$ = $\frac{3\sqrt {10}}{50}(125)^{\frac{3}{4}}$ = $7.09306$
b)
$CM^{\frac{3}{4}}$ = $2C0.5^{\frac{3}{4}}$
$M^{\frac{3}{4}}$ = $2\times0.5^{\frac{3}{4}}$
$M$ = $(2\times0.5^{\frac{3}{4}})^{\frac{4}{3}}$ = $1.25992$
The plant must acquire the difference = $1.25992-0.5$ = $0.75992$ $kg$
