Answer:
The time that will have to pass before one has under 1 oz of caffeine remaining is 24.53 hours
Explanation:
Here, we have the formula for half life as follows;
[tex]N(t) = N_0(\frac{1}{2})^{\frac{t}{t_{1/2}}[/tex]
Where:
N(t) = Remaining quantity of the substance = 1 oz
N₀ = Initial quantity of the substance = 30 oz
t = Time duration
[tex]t_{1/2}[/tex] = Half life of the substance = 5 hours
Therefore, plugging in the values, we have
[tex]1= 30(\frac{1}{2})^{\frac{t}{5}}[/tex]
[tex]\frac{1}{30} = (\frac{1}{2})^{\frac{t}{5}}\\ln(\frac{1}{30}) =\frac{t}{5} ln(\frac{1}{2})\\\frac{t}{5} = \frac{ln(\frac{1}{30}) }{ ln(\frac{1}{2})} = 4.91\\ t = 4.91 \times 5 = 24.53 \ hours[/tex]
The time that will have to pass before one has under 1 oz of caffeine remaining = 24.53 hours.
