A hypothetical metal alloy has a grain diameter of $2\mathrm{.}410-2mm.$ After a heat treatment

at $575C$ for $500$min, the grain diameter has increased to $7\mathrm{.}310-2mm.$ Compute the time

required for a specimen of this same material $($i$.$e$.,d0=2\mathrm{.}410-2mm)$ to achieve a grain

diameter of $5\mathrm{.}510-2mm$ while being heated at $575C.$ Assume the $n$ grain diameter

exponent has a value of $2\mathrm{.}2.$