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

Answer

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Answer

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

Steps

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 $t \approx \boxed{0.72}$.