Answer:
t=5.1 days
Step-by-step explanation:
We know that the formula is:
[tex]N = N_0e^{-kt}[/tex]
Where N is the amount of substance after a time t, [tex]N_0[/tex] is the initial amount of substance, k is the rate of decrease, t is the time in days.
[tex]k=0.1368\\N_0 =32[/tex]
We want to find the average life of the substance in days
The half-life of the substance is the time it takes for half the substance to disintegrate.
Then we equal N to 16 gr and solve the equation for t
[tex]16= 32e^{-0.1368t}[/tex]
[tex]0.5= e^{-0.1368t}[/tex]
[tex]ln(0.5)= ln(e^{-0.1368t})[/tex]
[tex]ln(0.5)= -0.1368t[/tex]
[tex]t= \frac{ln(0.5)}{-0.1368}\\\\t=5.1\ days[/tex]
