A quantity P obeys the exponential growth law P(t)=Ce^kt (t in years). Find the formula for P(t), assuming that the doubling time is 7 years & P(0)=100.

Question

anonymous · Answer

P(0) = 100 means 100 = C*1, so C = 100

anonymous · Answer

Would k = 7 because that's the doubling time ?

anonymous · Answer

wouldn't it mean that e^(k*7) = 2? since after 7 years, you have multiplied by 2?

anonymous · Answer

then ln2 = k*7, and k = (ln2)/7
Does that make sense?

anonymous · Answer

then when t = 14, e^((ln2/7)*14) = e^2ln2 = e^ln4 = 4
I think that's it. take your "doubling time and make it into a fraction of ln2/(doubling time) =k

anonymous · Answer

I kind of get it, let me work it out on paper. Thanks!

anonymous · Answer

hello again, the formula would be P(t) = 100e^(t*ln2/7)

anonymous · Answer

Why wouldn't it be 4 ?

anonymous · Answer

Oh , nevermind ! I got it . Thanks again !

anonymous · Answer

no, the 4 was just to test it because I haven't done these in a while

anonymous · Answer

Gotcha .