The function $P(t)=4\mathrm{.}6e^{0\mathrm{.}14t}$ takes t $,$ days since an algal culture was prepared, and gives $A,$ area covered by the culture $($in square centimeters$).$ Determine the derivative $P^{\text{'}}(t)$ and then use it to solve $P^{\text{'}}(t)=8,$ which gives the number of days required for the culture to reach a growth rate of $8$ square centimeters per day. Your answer needs to be accurate to two decimal places.