A radioactive element decays at a rate of 5% annually. there are 40 grams of substance present. How much substance remains after 30 years. (the nearest 10th)

When will the amount of substance drop below 20 grams (to the nearest year) ?

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