Question

Expressy as a function ofx. The constantC is a positive number.

$\ln y=-2x+\ln C$

Short answer

$y=C{e}^{-2x}$

Step-by-step solution

Step 1. Given information.

Consider the given information.

$\ln y=-2x+\ln C$

Step 2. Calculation.

Use the logarithm property to solve.

$\begin{array}{l}\ln y=-2x+\ln C\\ \ln y-\ln C=-2x\\ \ln \frac{y}{C}=-2x\\ \frac{y}{C}=e^{-2x}\\ y=C{e}^{-2x}\end{array}$

Step 3. Conclusion.

The obtained result is$y=C{e}^{-2x}$.