How much of a radioactive kind of xenon will be left after 15 days if the half-life is 5 days and you start with 96 grams

12 grams

Step-by-step explanation:

15/5 = 3 half lives

(1/2)³ = 1/8 of the original amount will remain

96 * 1/8 = 12 grams

Step-by-step explanation:

Radioactive decay problems are very similar to compound interest formulas, except the rate is subtracted from one, instead of adding to one.

I.e.

mass at time t, m(t) = M (1 - r)^(t/h)

where

M = initial mass (grams)

m (t) mass left at time t (grams)

h = half-life in number of days

r = 0.5 from "half-life"

t = time lapse in number of days

Here

M = 96

h = 5

t = 15

m(15) = 96(1-0.5)^(15/5)

= 96 (1/2)^3

= 12 grams