 Mathematics
2 June, 18:20

# 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) ?

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Answers (1)
1. 2 June, 19:47
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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
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