Question

Element X is a radioactive isotope such that every 18 years, its mass decreases by half. Given that the initial mass of a sample of Element X is 40 grams, how long would it be until the mass of the sample reached 24 grams, to the nearest tenth of a year?

Answer 1

A proportion would be useful. So we losing 40-24=16 grams. So if 18 — 20 then x — 16. You know what I mean? So 18*16/20 = 14.4y needed

Answer 2

It would be 13.3 years till the mass of the sample reached 24 grams.

What is exponential decay of a substance?

'A quantity is subject to exponentially decay if it decreases at a rate proportional to its current value.'

According to the given problem,

Let x be the number of years spent,

Initial mass = 40 grams

Final mass = 24 grams

Half-life = 18 years

⇒ 24 = 40 × $0.5^{\frac{x}{18} }$

⇒ 24/40 = 0.5^$\frac{x}{18}$

⇒ 3/5 = 0.5^$\frac{x}{18}$

Taking ln on both sides,

⇒ ln (3/5) = $\frac{x}{18}$ ln 0.5

⇒ ln (3/5) / ln (0.5) = x/18

⇒ x = ( 18 × ln (3/5) ) / ln (0.5)

⇒ x = 13.3 years

Hence, we can conclude that the sample need s 13.3 years to decrease its mass from 40 grams to 24 grams.

Learn more about exponential decay here: https://brainly.com/question/27492127

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