Question

Use the approximate​ half-life formula for the case described below. Discuss whether the formula is valid for the case described. Poaching is causing a population of elephants to decline by 7​% per year. What is the​ half-life for the​ population? If there are​ 10,000 elephants​ today, how many will remain in 50 ​years?

Answer 1

We first should calculate half-life.
half-life = elapsed time * log(2) / log (beginning amount / ending amount)
After 1 year there should be an elephant population of 9,300.
(10,000 - (10,000 * .07) = 10,000 - 700 = 9,300)

half-life = 1 year * log (2) / log (10,000 / 9,300)
half-life = 0.3010299957 / log ( 1.0752688172 )
half-life = 0.3010299957 / 0.0315170514
half-life = 9.5513375 years

Now, to calculate the remaining population after 50 years, we will use this formula:

Ending Amount = Beginning Amount / 2^n

where "n" = number of half-lives

So, for 50 years, the number of half-lives = 50 / 9.5513375 =
5.23487 half-lives

Ending Amount = Beginning Amount / 2^n
Ending Amount = 10,000 / 2^5.23487
Ending Amount = 10,000 / 37.658
Ending Amount = 265.5478
Ending Amount = 266

Source:
http://www.1728.org/halflife.htm