# Thread: Need help understanding this question

1. ## Need help understanding this question

The half life of Polonium-210 is 140 day and a sample of this element has a mass of 300 mg

Find the mass that remains after t days

y= f(t)
initial amount is 300 mg

f(t)= 300e^kt

To determine the value of k we use the fact that half life is 140d and so
f(140)= 150 thus

300e^140k=150

I am confused on how they get f(140) = 150?
since f(140)=300e^140k=/= 150??

2. By the definition of half life, after 140 days the mass of the radioactive substance is half that at time 0.

ie. $f(140)=\frac{300}{2}=150$

3. Its safe to say that:

$
m(t) = \frac {300}{2^\frac {t}{140}}
$

Hope this helps.