Question

A 18 gram sample of a substance that’s used to detect explosives has a k-value of 0.1226

Find the substance’s half-life in days
Round your answer to the nearest tenth

Answer 1

Answer: 5.7

I just did the test and got it correct

Answer 2

Given:
Initial mass = 18 g
k-value = 0.1226

The mass at time t (days) is

`m(t)=18e^(-0.1226t)`

At half life, m = 18/2 = 9 g.
The time for half life is given by

`9 = 18e^(-0.1226t)`
Therefore
ln(1/2) = -0.1226t

Hence obtain
t = ln(1/2) / -0.1226
= 5.654 days

Answer: 5.7 days (nearest tenth)