Question 609841
an isotope of strontium 90 has a half life of 38 years. if you have 500 mg of this isotope today, how many milligrams (to the nearest tenth) will you have in 19 years?
exponential growth/decay equation
{{{A = Aoe^(kt)}}}
where
A is amount after time t
Ao is the initial amount
k is the growth/decay constant
t is time
.
From: "an isotope of strontium 90 has a half life of 38 years." we can determine k:
{{{.5Ao = Aoe^(k*38)}}}
dividing both sides by Ao:
{{{.5 = e^(k*38)}}}
{{{ln(.5) = 38k}}}
{{{ln(.5)/38 = k}}}
{{{-.01824 = k}}}
.
Now, we can answer:
if you have 500 mg of this isotope today, how many milligrams (to the nearest tenth) will you have in 19 years?
starting with:
{{{A = Aoe^(-.01824t)}}}
{{{A = 500e^(-.01824*19)}}}
{{{A = 500(.7071)}}}
{{{A = 354.55}}} mg