Question

Situation:A 33 gram sample of a substance that'sused for drug research has a k-value of0.1124.-ktN = NoeNo 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

6.2 days

Step-by-step explanation:

The half-life occurs when the mass N is equal to half of the initial mass, so to find the half-life, we need to replace N with No and solve for t

`\begin{gathered} N=N_oe^(-kt) \\ N=N_oe^(-0.1124t) \\ \\ \text{ Replacing N = No/2, we get} \\ (N_o)/(2)=N_oe^(-0.1124t) \\ \\ \text{ Solving for t} \\ (N_o)/(2N_o)=e^(-0.1124t) \\ \\ (1)/(2)=e^(-0.1124t) \\ \\ ln((1)/(2))=ln(e^(-0.1124t)) \\ \\ -0.6931=-0.1124t \\ \\ (-0.6931)/(-0.1124)=(-0.1124t)/(-0.1124) \\ \\ 6.2\text{ days = t} \end{gathered}`

Therefore, the answer is

t = 6.2 days