Question

The half-life of a radioactive substance is the time it takes for a quantity of the substance to decay to half of the initial amount. The half-life of the radioactive gas radon is approximately 2.8 days. The initial amount of radon used in an experiment is 74 grams. If N represents the number of grams of radon remaining t days after the start of the experiment,

Answer 1

N = 74(1/2)^(t/2.8)

Explanation:

The exponential function expressing a half-life relation can be written ...

amount = (initial amount) × (1/2)^(t/(half-life))

For the numbers given in this problem, this is ...

N = 74(1/2)^(t/2.8)

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Some folks like to express these relations in the form ...

N = 74e^(-kt)

In this form, the value of k is ...

k = ln(2)/(half-life) ≈ 0.693147/2.8 ≈ 0.24755

N = 74e^(-0.24755t)