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## Element X is a radioactive isotope such that every 9 years, its mass decreases by half. Given that the initial mass of a sample of Element X

Question

Element X is a radioactive isotope such that every 9 years, its mass decreases by half. Given that the initial mass of a sample of Element X is 70 grams, how long would it be until the mass of the sample reached 56 grams, to the nearest tenth of a year?

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Mathematics
6 months
2021-07-31T11:03:36+00:00
2021-07-31T11:03:36+00:00 1 Answers
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## Answers ( )

Answer:

2.9 years

Step-by-step explanation:

Given that :

Half-life t1/2 = 9 years

Initial mass = I = 70 grams

A = final mass = 56 grams

t = time taken to reach final amount

Using the exponential half life relation :

A = I(0.5)^t/t1/2

56 = 70(0.5)^t/9

56/70 = 0.5^t/9

0.8 = 0.5^t/9

Log 0.8 = log 0.5^t/9

−0.096910 = −0.301029 * t/9

t/9 = 0.096910 / 0.301029

t/9 = 0.3219291

t = 0.3219291 * 9

t = 2.8973619

t = 2.9 years