Answer:
First problem: 89.07 grams
Second problem: 3910.15 days
Step-by-step explanation:
We can solve these problems with the exponencial equation:
P = Po * (1+r)^t
Where P is the final value, Po is the inicial value, r is the rate and t is the time.
In the first problem, the half-life is 119.77 days and Po = 100, so we have that:
P = 100 * (1-0.5)^(t/119.77)
So after 20 days, we will have:
P = 100 * (1-0.5)^(20/119.77) = 89.07 grams
For the second problem, we have the half-life of 5730 days, and the final value over the inicial value is 62.31%, so:
P/Po = (1-0.5)^(t/5730)
0.6231 = 0.5^(t/5730)
log(0.6231) = log(0.5^(t/5730))
-0.4730 = (t/5730)*log(0.5)
-0.4730 = (t/5730)*(-0.6931)
(t/5730) = 0.6824
t = 0.6824 * 5730 = 3910.15 days
