Half-life question

Question

Suppose that a severe virus is impacting a bee colony and the population of bees has a half-life of 5 days.

What percentage of the original bee colony would be surviving after 15 days of decay, if the rate of decay is 14% a day?
__________%
(Round to two decimals.)

Answer 1

For P(t) = P(0)e^-kt,

 

k = ln(0.5) / t_1/2 = ln(0.5) / 5 = 0.1386 days^-1

 

P(15) = 100e^-(0.1386*15) = 12.5

 

12.5% survive after 15 days

 

 

Another (and simpler) way to do this:

 

After 15 days = 3*5 days = 3 half-lives, you are left with (1/2)³ as many bees as when you started

 

Start with 100% ⇒ left with (1/2)³*100% = 12.5%

Answer 2

A = a₀(0.5)^t/h

A = a₀(0.5)^15/5

A = a₀(0.5)³

 

Can you calcuilate?