WOW! 9 syllable words again. Can you say the same thing so that someone who has not spent years studying this can begin to understand this? Basic English.
Given that P(t) = P(0)e^(kt) then the doubling time can be determined by:
P(t)/P(0) = 2 = e^(kt)
ln(2) = kt
t = ln(2)/k, or k = ln(2)/t
Hank, I used no words with nine syllables. The word with the most syllables I did use was "exponentially," which has five syllables. This is only one more syllable than the longest word you used: "mathematics."
Exponential growth uses algebra and logarithms, both of which are taught at a high-school level. It is the same formula as continuously compounding interest.