find half life of caffeine

Question

The half-life of caffeine is approximately 5.7 hours. If there are 30mg of caffeine in a half cup of coffee ice cream, how long will it take to decrease to 5mg of caffeine?

Answer 1

Formula you will need:

N(t) = N₀ (.5) ^t/t1/2

where:

N(t) = Quantity of Substance

N₀ = Initial Quantity of Substance

t = Time elapsed

t_1/2 = half life of Substance

The variables for this problem are:

t_1/2 = 5.7hrs

N₀ = 30mg

N(t) = 5mg

Therefore your formula should look like this:

N(t) = N₀ (.5) ^t/t1/2

5 = 30 (.5) ^t/5.7

t = [t_1/2 ln (N(t)/N₀)] / (-ln2)

t = [5.7 ln (5/30)] / (-.69)

t = [5.7 ln .17] / -.69

t = -10.10 / -.69

t = 14.64 if averaged throughout (14.7342 is more accurate with no averages)