Answer:
Option B - 3.75 mg
Step-by-step explanation:
Given : Polonium-218 has a half-life of about 3 minutes.
To find : After 15 minutes, how many milligrams of a 120 mg sample will remain?
Solution :
Considering an exponential model,
[tex]y=a_0(x)^\frac{t}{n}[/tex]
Where, y is the total amount
[tex]a_0[/tex] is the original amount [tex]a_0=120[/tex]
x is the half-life of Polonium-218 [tex]x=\frac{1}{2}=0.5[/tex]
t is the time taken t=15 minutes
n is the time spent n=3 minutes
Substitute the values in the exponential model,
[tex]y=120(0.5)^{\frac{15}{3}}[/tex]
[tex]y=120(0.5)^5[/tex]
[tex]y=120(0.03125)[/tex]
[tex]y=3.75[/tex]
Therefore, Option B is correct.
3.75 mg is required amount.
