# The population of a herd of sheep declines exponentially. If it takes 3 years for 15% to decline then how long will it take for half the population to decrease ?

##### 1 Answer

Mar 14, 2017

It would take 12.8 years.

#### Explanation:

Let initial number of sheep

Let the number of sheep remaining after time t

The equation for exponential decay gives us:

If the number of sheep have declined by 15% then the number remaining must be 85% of the original total.

So

Putting in the numbers:

Taking natural logs of both sides gives:

I won't go into the derivation here but it can be shown that the expression for 1/2 life in terms of the decay constant **k** is given by: