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?

A. 5 mg

B. 12 mg

C. 40 mg

D. 194 mg

Answer 1

the answer is a

Explanation:

Answer 2

Option A = 5 mg

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)^{(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)^{(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.