The problem is to solve the equation $93 = 100 - 100e^{-0.07x}$ for $x$, and give the answer to 3 decimal places.

1. Problem Description

The problem is to solve the equation $93 = 100 - 100e^{-0.07x}$ for $x$, and give the answer to 3 decimal places.

2. Solution Steps

First, we isolate the exponential term:

$93 = 100 - 100e^{-0.07x}$

$100e^{-0.07x} = 100 - 93$

$100e^{-0.07x} = 7$

$e^{-0.07x} = \frac{7}{100}$

$e^{-0.07x} = 0.07$

Next, we take the natural logarithm of both sides:

$\ln(e^{-0.07x}) = \ln(0.07)$

$-0.07x = \ln(0.07)$

Finally, we solve for $x$:

$x = \frac{\ln(0.07)}{-0.07}$

$x = \frac{-2.65926}{-0.07}$

$x \approx 37.989$

Rounding to 3 decimal places, we get $x \approx 37.989$.

3. Final Answer

37.989