Question

Situation:A 22 gram sample of a substance that'sused to sterilize surgical instruments hasa k-value of 0.138.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

Step-by-step explanation

Given that the initial sample has a mass of 22 grams and that its k-value is 0.138, We can use the formula below to find its half-life.

`N=N_0e^(-kt)`

At half life, the substance decays to half of itself, therefore;

`\begin{gathered} (22)/(2)=22e^(-0.138t) \\ 11=22e^(-0.138t) \\ divide\text{ both sides by 22} \\ (11)/(22)=e^(-0.138t) \\ 0.5=e^{\left\{-0.138t\right\}} \\ ln0.5=ln(e^(-0.138t)) \\ \ln \left(0.5\right)=-0.138t \\ t=-(\ln \left(0.5\right))/(0.138) \\ t=5.02280\approx5.0days \end{gathered}`

Answer: 5.0 days