The formula $A=24\mathrm{.}2e^{0\mathrm{.}0778t}$ models the population of a US state, $A,$ in millions, $t$ years after $2000.$ Determine algebraically when the population was predicted to reach $31\mathrm{.}4$ million.

The population of the state will reach $31\mathrm{.}4$ million in the year

$($Round up to the nearest year.$)$