Question

A sample of bacteria is decaying according to a half-life model. If the sample begins with 80 bacteria and after 10 hours or 20 bacteria, what is the approximate half life and hours round to the nearest integer.

Answer 1

5 hours

Explanation:

After 10 hours, the number of bacteria drops from 80 to 20. That's a factor of ¼, so 2 half lives must have passed (½ × ½ = ¼). If 10 hours equals 2 half lives, then 1 half life is 5 hours.

We can show this with the half life equation:

A = A₀ (½)^(t / T)

20 = 80 (½)^(10 / T)

¼ = (½)^(10 / T)

10 / T = 2

T = 5