Answer:
In 30 years the mass of the element will be approximately 8.6 grams and it'll take approximately 14 years to drop below 20 grams.
Step-by-step explanation:
Since it is decaying at 5% anually we can model it's mass as a compounded interest with a negative rate. This is shown below:
final mass = initial mass*(1 - r)^t
Where r is the rate of decay and t is the elapsed time. Applying the data from the question we have:
After 30 years:
final mass = 40*(1 - 0.05)^30
final mass = 40*(0.95)^30 = 8.5855 grams
The time it'll take to reach 20 grams:
20 = 40*(0.95)^t
0.95^t = 0.5
ln(0.95^t) = ln(0.5)
t*ln(0.95) = ln(0.5)
t = ln(0.5)/ln(0.95) = 13.5134
