A certain type of star emits energy according to the formula $E=150\cdot {10}^{0.5M}$, where $E$ is the energy in joules and $M$ is the magnitude of the star's brightness. Calculate the energy emitted by stars of magnitude $2$, $4$, $6$, and $8$. Then, plot the points on the graph and connect them through a smooth curve.

Calculate the derivative of the function $f\left(x\right)=\ln \left({(2x-3)}^5\right)$.

In a newly established wildlife reserve, $100$ rabbits are introduced into an area with an estimated carrying capacity of $10,000$ rabbits. A logistic model of the rabbit population is given by $R(t) = \frac{1,000,000}{100 + 9900 e^{-0.3t}}$, where $t$ is measured in years. Plot the graph of the derivative of $R$ and determine the year when the population is growing fastest. Round the answer to 2 decimal places.