Question

A 50 gram sample of a substance that's

used to treat thyroid disorders has a k

value of 0.1137.

Answer 1

The question is incomplete. Here is the complete question.

A 50 gram sample of a substance that's used to treat thyroid disorders has a k-value of 0.1137. Find the substance's half-life, in days. Round your answer to the nearest tenth.

Answer:
`t_(1/2)` = 6.1 days

Explanation: Half-life is the amount of time necessary for a substance to reduce to half of its initial value.

To determine half-life through mass of a substance:

`N = N_(0).e^{-kt_(1/2)}`

Initially, there are 50 grams. After 1 half-life, there are 25 grams:

`25 = 50.e^{-0.1137.t_(1/2)}`

`(25)/(50) = e^{-0.1137.t_(1/2)}`

`(1)/(2) = e^{-0.1137.t_(1/2)}`

`ln ((1)/(2) ) = ln (e^{-0.1137.t_(1/2)})`

ln(1) - ln(2) = -0.1137.
`t_(1/2)`

`t_(1/2) = (- ln(2))/(- 0.1137)`

`t_(1/2) =` 6.1

The half-life of the sample substance is 6.1 days.