$5\mathrm{.}7$ An ultra$-$high pressure $($UHP$)$ process is being used to process a fruit juice containing a pathogen with a rate constant $(k)$ of $\frac{0\mathrm{.}652}{m}in$ at $400$MPa, and an activation volume constant of $3\mathrm{.}5{10}^{-5}\frac{m^3}{m}$ole. Determine the process time required at $350$MPa if the initial population of the pathogen is $5$ per container and the probability of survivors is ${10}^{-7}.$