I am learning calculus from a book of mine, and it gave an example problem of exponential growth (as derived from the exponential differential equation of dy/dx = ky to be y=Ce^kt) saying a population is growing at a rate of 2% per year, and says that K, the growth constant, in this case is k = .02. My confusion is, I thought you could set up the equation of this to be Y=A(1.02)^(t) "A" being the initial amount, and here I can see it is also Y=A*e^(.02*t) since k=.02 yet these equations are not the same and I am very confused because if you plug in one year length (t=1) then the initial amount has grown by 1.02 (or increased by 2%) and this is not the case for the second equation. Could someone explain to me whether the book has set k to the wrong value (if an amount grows by x% by some time, the growth constant k is not that percentage) or why these equations are different, or if one is incorrect.(adsbygoogle = window.adsbygoogle || []).push({});

(The book says an amount is growing by 2% and then says that the growth constant k=.02)

**Physics Forums | Science Articles, Homework Help, Discussion**

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Exponential growth constant

**Physics Forums | Science Articles, Homework Help, Discussion**