A=pe^kt

ln(A) = ln(pe^kt) = ln(p) + ln(e^kt) log (xy) = log(x) + log(y)

ln(A) = ln(p) + kt

log_{e}(e^{n}) = n log_{e}(e) ; log_{e}(e) = 1

t = [ln(A) - ln(P)]/k