The equation for time dilation is:
[unparseable or potentially dangerous latex formula].
Plugging in, say, .5c for [unparseable or potentially dangerous latex formula] gives:
[unparseable or potentially dangerous latex formula],
which means that the observed time between events for an observer moving with a constant velocity of [unparseable or potentially dangerous latex formula] is greater than the observed time for a stationary observer. However, time is supposed to slow down the faster you move (for example, astronauts age less, by a very slight amount, than those who remain on Earth.) Why is this so? The equation seems to imply that observed time increases the faster you move. What am I interpreting incorrectly here?