Answered

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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.

SituationA9 Gram Sample Of A Substance Thatsused For Drug Research Has A Kvalue Of01459NNoektNoinitial Mass At Time T 0Nmass At Time Tk A Positive Constant That class=

Sagot :

Given:

Initial value = 9 grams

k-value = 0.1459

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

Apply the formula:

[tex]N=N_0e^{-kt}[/tex]

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

[tex]\begin{gathered} \frac{N_0}{2}=N_0e^{-kt} \\ \\ \frac{1}{2}=e^{-kt} \end{gathered}[/tex]

Plug in 0.1459 for k and solve for t.

We have:

[tex]\begin{gathered} \frac{1}{2}=e^{-0.1459t} \\ \\ \end{gathered}[/tex]

Take the natural logarithm of both sides:

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

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

ANSWER:

4.8 days

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