Question

Situation: a 25 gram sample of a substance that’s used for drug research has a K-value of 0.1205

N0(zero)= initial mass(at time t=0)
N= mass at time t
K= a positive constant that depends on the substance itself and on the units used to measure time
t= time, in days
Find the substances half-life, in days. Round your answer to the nearest tenths????

Answer 1

The decay model is given as


`N=N_0e^(-Kt)`

The substance's half-life is the time it takes for the substance to decay to half its original amount. In other words, it's the time
`t` such that
`N=\frac{N_0}2`. Substituting into the model, you have


`\frac12=e^(-Kt)`

You can solve for
`t` now.


`\frac12=e^(-Kt)`

`\implies\ln\frac12=\ln e^(-Kt)`

`\implies-\ln2=-Kt\ln e`

`\implies\frac{\ln2}K=t\approx5.7523\text{ days}`