What happens to units in an exponent?
My math textbook just introduced the exponential equation:
$$A_t = Pe^{rt}$$
I've always made it a point in solving math problems to include the units in every calculation.
After I plug in my values:
$$A_{9 years} = $980e^{.07(9 years)}$$
...and simplify:
$$A_{9 years} = $980e^{.63 years}$$
I end up with a unit in my exponent: $e^{.63 years}$
I'm pretty sure this is insolvable, as both Wolfram|Alpha, and Google wouldn't give me an answer. So is this a bad equation?
Units in exponents don't make sense. Instead, this hints to the fact that $r$ should have a unit like ${\mathrm s}^{-1}$ so that $rt$ is dimensionless. ($P$ again will carry the unit of whatever this expression calculates in the end).