Question

A 29 gram sample of a substance thats used for drug research has a k-value of 0.1359.

N=Noe^-kt
No=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 substance's half-life,in days.Round your answer to the nearest tenth.

Answer 1

\[n=n_0e^{-kt}\\\]

Answer 2

im still confused

Answer 3

\[n=n_0 e^{-0.1359t}\\n=0 \rightarrow n_0=n_0 e^0=29 gr\\n_0=29\\n=29* e^{-0.1359t}\]

Answer 4

for a half life
solve n=n0/2
\[n=29* e^{-0.1359t}=\frac{n_0}{2}=\frac{29}{2}\\ e^{-0.1359t}=\frac{1}{2}\\ln\\ln( e^{-0.1359t})=\ln(\frac{1}{2})\\0.1359t=-0.6931\\t=5.100\]

Answer 5

\[t \approx 5\]