Answer:
[tex]t_{1/2}=45.09 d[/tex]
Step-by-step explanation:
We can use the decay equation:
[tex]M=M_{0}e^{-\lambda t}[/tex]
- M(0) is the initial mass
- M is the mass after t (1000 days) time
- λ is the decay constant
But:
[tex]\lambda = ln(2)/t_{1/2}[/tex]
So, we can rewrite the initial equation:
[tex]M=M_{0}e^{-\frac{ln(2)}{t_{1/2}}t}[/tex]
Now, we just need to solve it for t(1/2):
[tex]ln(\frac{M}{M_{0}})=-\frac{ln(2)}{t_{1/2}}t[/tex]
[tex]t_{1/2}=-\frac{ln(2)}{ln(\frac{M}{M_{0}})}t[/tex]
[tex]t_{1/2}=-\frac{ln(2)}{ln(\frac{10.75}{50})}100[/tex]
[tex]t_{1/2}=45.09 d[/tex]
I hope it helps you!
