The number of computers infected in $t$ seconds can be modelled by the function $N(t)$, where

$$N(t)=2^{t/8.5}.$$

This is a reasonable model. In the beginning (when $t=0$) we assume that the worm has infected only $1$ computer, and indeed, $N(0)=1$. In 8.5 seconds, the number becomes $N(8.5)=2$, so it doubles. In another $8.5$ seconds, $N(17)=4$. This doesn’t sound like very fast growth, but at the end of one minute ($t=60$) the number becomes more than $133$. In two minutes, $28995$ computers are infected, and in $5$ minutes, the number of computers infected is in the billions. Which means that the rate of growth must have slowed down, because there aren’t so many computers in the world! I hope this helps you understand why it caused the slowdown of the Internet traffic in Korea.

$N(t)$ is an example of an exponential function, which increases very fast. The prototypical example is THE exponential function, $f(x)=e^x$. Here the number e is an irrational number (just like the famous $\pi$, whose value is approximately $2.7182818\dots$. The graph of the function (made using desmos.com) is as follows.

The exponential function is not symmetric across the $y$-axis, nor across the origin. That is to say, it is not an even function or an odd function. However, consider the functions:

$$E(x)=(e^x+e^{-x})/2,$$ and $$O(x)=(e^x-e^{-x})/2.$$ $E$ is an even function, and $O$ is an odd function, and the exponential function is the sum of these functions. Draw the function $E(x)$ from $x=-5$ to $x=5$ using MS-Excel (update: try www.desmos.com), and see what the graph looks like. Does it look like a clothesline secured at its two ends?

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