Question

a 34 gram sample of a substance that's used to treat thyroid disorders has a k-value of 0.137. find the substance's half-life, in days. round to the nearest tenths.

Answer 1

5.1 days

Explanation:

Given in the question,

initial amount of substance = 34 grams

k-value = 0.137

To find the half life of this substance we will use following formula

`N(0)/2 = N(0)e^(-kt)`

here N(0) is initial amount of substance

t is time in days

Plug values in the formula

`34 /2 = 34e^(-0.137t)`

1/2 = e^{-0.137t}

Take logarithm on both sides

ln(1/2) = ln( e^{-0.137t})

ln(1/2) = -0.137t

t = ln(1/2) / -0.137

t = 5.059

t ≈ 5.1 days (nearest to tenths)