Questions: Solve for r to two decimal places. 5=e^(3r) r ≈ (Do not round until the final answer. Then round to the nearest hundredth as needed.)

Solution Steps

The general form of the equation is $k = e^{m r}$, where $k$ and $m$ are constants.

Taking the natural logarithm of both sides gives us $\ln(k) = \ln(e^{m r})$.

Using the property that $\ln(e^x) = x$, we simplify the right side to $m r$.

After simplification, we have $\ln(k) = m r$.

Solving for $r$ gives $r = \frac{\ln(k)}{m} = \frac{\ln(5)}{3} = 0.54$.

Final Answer: The value of $r$ rounded to 2 decimal places is 0.54.