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##### I am struggling with my precalculs homework. Can you help me get started?

label Calculus
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Suppose that 10 grams of Carbon is released in a nuclear energy plant accident.  How  long will it take for the 10 grams to decay to 1 gram?

Oct 22nd, 2017

It seems that you mean Carbon-14, a radioactive isotope of carbon with half life of 5730 years. The amount of radioactive substance can be expressed by the law m(t) = m_0 (1/2)^(t/T) where m_0 is the initial mass, T is the half life. We have 1 = 10*(1/2)^(t/5730); 2^(t/5730) = 10. Take logarithm by the base 10 of both sides of the equation: (t/5730)*log(2) = log(10) = 1; t = 5730 / log(2) = 19000 years.

Apr 13th, 2015

Thanks, that has helped me a lot.

Apr 13th, 2015
Apr 13th, 2015

Your project contains essentially the same exponential model for radioactive decay, the only difference being the form of the expression: y = Ce^(kt); C = 10.

Assuming that the half life is 5715 years, we get 5 = 10*e^(5715k); e^(5715k) = 5/10 = 1/2;

5715 k = ln(1/2) = -0.6931, and k = -0.6931/5715 = -1.213*10^{-4}.

The function is y = 10e^(-0.0001213 t) and equals 1 if e^(-0.0001213 t) = 1/10 = 0.1.

Then -0.0001213 t = ln(1/10) = -2.303, and t = 2.303/0.0001213 = 18990 years.

Apr 13th, 2015

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Oct 22nd, 2017
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Oct 22nd, 2017
Oct 22nd, 2017
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