, therefore years.
, so half-times, and that is years.
, so and years.
half-times, so days.
half-times, so days.
, so a little less than days.
, so .
, therefore and days.
The growth percentage is , so the growth factor is .
The doubling time is defined as , so . This gives you , so and from that you can derive the above formula.
gives you .
gives you .
gives you and therefore .