The problem asks us to solve the equation $60 = \frac{75}{1 + 5e^{-0.3x}}$ for $x$, and give the answer correct to 3 decimal places.

1. Problem Description

The problem asks us to solve the equation $60 = \frac{75}{1 + 5e^{-0.3x}}$ for $x$, and give the answer correct to 3 decimal places.

2. Solution Steps

First, we multiply both sides of the equation by $1 + 5e^{-0.3x}$:

$60(1 + 5e^{-0.3x}) = 75$

Divide both sides by 60:

$1 + 5e^{-0.3x} = \frac{75}{60} = \frac{5}{4} = 1.25$

Subtract 1 from both sides:

$5e^{-0.3x} = 1.25 - 1 = 0.25$

Divide both sides by 5:

$e^{-0.3x} = \frac{0.25}{5} = 0.05$

Take the natural logarithm of both sides:

$\ln(e^{-0.3x}) = \ln(0.05)$

$-0.3x = \ln(0.05)$

$x = \frac{\ln(0.05)}{-0.3}$

$x = \frac{-2.995732}{-0.3} \approx 9.985773$

Rounding to 3 decimal places, we have $x \approx 9.986$.

3. Final Answer

$x = 9.986$