What does mean? I assume the "1/4" is a subscript saying "the value of t at which A is 1/4 its original value". If so there is NO "t" in the equation. There is and that is what you want to solve for.
You have been fooled by your own notation! You have multiplied by 4 as if meant that t had been multiplied by 1/4.
What am I doing wrong here? The answer is allegedly 1.386/k
However, this answer key has been wrong before. Can someone please confirm/deny this?