Dimensions of the Argument of an Exponential

why the power of a exponential function shouldnt have units.. for example e^(-kt) is some function where t is time so we conclude that k has units of inverse of time why?
- skand (age 17)
India

Think back to what an exponential means. Say take 5^3. That means 5x5x5. The exponent tells you how many of the multiplier are there. What would it mean to have "3 meters" of some factor? Only a plain number makes sense.  When you generalize exponents to include real numbers, not just integers, you still need something that makes sense for at least the integers, so you still need for the exponents to be plain numbers without dimensions.

Mike W.

(published on 02/19/2014)