Question

Situation:A9 gram sample of a substance that'sused for drug research has a k-value of0.1459.N-Noe-ktNo-initial mass (at time t = 0)N-mass at time tk= a positive constant that depends onthe substance itself and on the unitsused to measure timet-time, in daysFind the substance's half-life, in days.Round your answer to the nearest tenth.

Answer 1

Given:

Initial value = 9 grams

k-value = 0.1459

Let's find the substance's half-life in days.

Apply the formula:

`N=N_0e^(-kt)`

The half-life of a substance can be expressed as:

`\begin{gathered} (N_0)/(2)=N_0e^(-kt) \\ \\ (1)/(2)=e^(-kt) \end{gathered}`

Plug in 0.1459 for k and solve for t.

We have:

`\begin{gathered} (1)/(2)=e^(-0.1459t) \\ \\ \end{gathered}`

Take the natural logarithm of both sides:

`\begin{gathered} ln((1)/(2))=-0.1459t\text{ ln\lparen e\rparen} \\ \\ −0.693147=-0.1459t \\ \\ t=(−0.693147)/(-0.1459) \\ \\ t=4.75\approx4.8\text{ days} \end{gathered}`

Therefore, the substance's half-life in days is 4.8 days.

ANSWER:

4.8 days