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: [tex]t_{1/2}[/tex] = 6.1 days
Step-by-step 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:
[tex]N = N_{0}.e^{-kt_{1/2}}[/tex]
Initially, there are 50 grams. After 1 half-life, there are 25 grams:
[tex]25 = 50.e^{-0.1137.t_{1/2}}[/tex]
[tex]\frac{25}{50} = e^{-0.1137.t_{1/2}}[/tex]
[tex]\frac{1}{2} = e^{-0.1137.t_{1/2}}[/tex]
[tex]ln (\frac{1}{2} ) = ln (e^{-0.1137.t_{1/2}})[/tex]
ln(1) - ln(2) = -0.1137.[tex]t_{1/2}[/tex]
[tex]t_{1/2} = \frac{- ln(2)}{- 0.1137}[/tex]
[tex]t_{1/2} =[/tex] 6.1
The half-life of the sample substance is 6.1 days.
