Explanation

(d) Radius of $n^{th}$ orbit $r_{n} \propto n^{2}$, graph between $r_{n}$ and $n$ is a parabola. Also, $\frac{r_{n}}{n_{1}} = \left( \frac{n}{1} \right)^{2} \Rightarrow \log_{e}{\left( \frac{r_{n}}{r_{1}} \right) = 2\log_{e}{(n)}}$
Comparing this equation with $y = mx + c$
Graph between $\log_{e}\left( \frac{r_{n}}{r_{1}} \right)$ and $\log_{e}{(n)}$ will be a straight line, passing from origin
Similarly it can be proved that graph between $\log_{e}\left( \frac{f_{n}}{f_{1}} \right)$ and $\log_{e}n$ is a straight line. But with negative slope