A certain element decays at a constant rate of 3% per year.If you start with 15 grams of the element, how long will it take before there are only three grams left?a.)52.8 yearsb.)51.8 yearsc.)54.4 yearsd.)53.4 years
Question
A certain element decays at a constant rate of 3% per year.If you start with 15 grams of the element, how long will it take before there are only three grams left?a.)52.8 yearsb.)51.8 yearsc.)54.4 yearsd.)53.4 years
Solution
This problem can be solved using the formula for exponential decay, which is:
N = N0 * e^(-λt)
where: N is the final amount of the substance, N0 is the initial amount of the substance, λ is the decay constant, and t is the time.
In this case, we know that N = 3 grams, N0 = 15 grams, and λ = 0.03 per year. We want to solve for t.
Rearranging the formula to solve for t gives us:
t = -ln(N/N0) / λ
Substituting the given values into this formula gives us:
t = -ln(3/15) / 0.03
Calculating this gives us:
t ≈ 54.4 years
So, the answer is c.) 54.4 years.
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