Answer
If the number increases geometrically it is worse.
Work Step by Step
The number of students increasing geometrically is worse than the number of students increasing arithmetically.
Example: Suppose first day only one student is affected.
Now, suppose that\[d=2\] for arithmetically increasing of affected students.
The number of student affected after 30 days will be:
\[\begin{align}
& {{S}_{n}}=\frac{n}{2}\left[ 2a+\left( n-1 \right)d \right] \\
& =\frac{30}{2}\left( 2+29\times 2 \right) \\
& =15\times 60 \\
& =900
\end{align}\]
Let \[r=2\] for geometric increase of number of affected students
The number of student affected after 30 days will be:
\[\begin{align}
& {{S}_{n}}=\frac{a\left( {{r}^{n}}-1 \right)}{\left( r-1 \right)} \\
& {{S}_{n}}=\frac{1\left( {{2}^{30}}-1 \right)}{\left( 2-1 \right)} \\
& =\left( {{2}^{30}}-1 \right) \\
& {{S}_{n}}=1073741827
\end{align}\]
If the number increases geometrically it is worse.
