Question

Terbium-160 has a half-life of about 72 days. After 396 days, about how many milligrams of a 220 mg sample will remain?

Answer 1

C....................

Answer 2

Answer:

Option A = 5 mg  

Step-by-step explanation:

Given : Terbium-160 has a half-life of about 72 days.

To find : After 396 days, about how many milligrams of a 220 mg sample will remain?

Solution :

We have given the Terbium-160 has a half-life of about 72 days.  

We can represent the situation with an exponential function,

$A_t = A_0(0.5)^{\frac{t}{n}}$

Where,

$A_t$ is the amount at any time t,

$A_0=220$ is the original amount,

n=72 is the half-life

t=365 number of days

Substituting all the values,

$A_t =220(0.5)^{\frac{396}{72}}$

$A_t =220(0.5)^{5.5}$

$A_t =220(0.022)$

$A_t =4.84$

Approximately 4.84=5 mg

Therefore, Option A is correct.  

After 396 days, there will only be 5 mg of Terbium-160.