A = Pe^(rt)
Let A = 2P
Let r = 0.03
2P = Pe^(0.03t)
We need to find t.
2P/P = e^(0.03t)
2 = e^(0.03t)
Take the natural log on both sides.
ln(2) = ln(e^(0.03t)
ln(2) = 0.03t
ln(2)/0.03 = t
23.1049060187 = t
You did not indicate what we are talking about. I will assume weeks or months.
So, t is about 23 weeks or 23 months.