Solve for $t$. \[ e^{-0.88 t}=0.53 \]

Step 1 ：We are given the equation \(e^{-0.88 t}=0.53\).

Step 2 ：We take the natural logarithm (ln) on both sides of the equation to get \(-0.88t = \ln(0.53)\).

Step 3 ：We then solve for \(t\) by dividing both sides of the equation by \(-0.88\).

Step 4 ：Doing this, we find that \(t = \frac{\ln(0.53)}{-0.88}\).

Step 5 ：Calculating the right side of the equation, we find that \(t \approx 0.72\).

Step 6 ：Final Answer: The solution to the equation \(e^{-0.88 t}=0.53\) is \(t \approx \boxed{0.72}\).