Half-Life #10-11

Question

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

 

What approximate daily percentage of decay does the bee colony demonstrate?

% (Round to two decimals.)
(Hint: use the Rule of 70 backwards by dividing by the half-life period instead of the rate.)

 

 What percentage of the original bee colony would be surviving after 13 days of decay?

% (Round to two decimals.)

Answer 1

The rule of 70 generally says that the time it takes for a quantity to double multiplied by the growth rate is approximately equal to 70.

 

The same rule can be applied to situations where the number is declining.  The half-life (the time it takes for the quantity to decrease by half) times the rate of decay is also approximately equal to 70.

 

So in this case, the half-life is 5 days, so the percentage decay per day is 70 / 5 = 14% per day.

 

To find the percentage surviving after 13 days, use the formula P = 100 * (1-r/100)ⁿ , where P is percentage remaining, r is the decay rate per day (as a percentage) and n is the number of days.

 

So P = 100*(1-14/100)¹³ = 100 * .86¹³ = 14.07% (rounded to two decimals).