Answer:
Step-by-step To solve the equation \(50e^{-0.14x} = 40\), we'll first isolate \(e^{-0.14x}\) by dividing both sides by 50:
\[e^{-0.14x} = \frac{40}{50} = 0.8\]
Next, take the natural logarithm (ln) of both sides to solve for \(x\):
\[-0.14x = \ln(0.8)\]
Now, solve for \(x\):
\[x \approx \frac{\ln(0.8)}{-0.14} \approx 11.003\]
Rounded to three decimal places, \(x \approx 11.003\).: