Time remaining:
I am struggling with my precalculs homework. Can you help me get started?

Calculus
Tutor: None Selected Time limit: 3 Days

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?

Apr 13th, 2015

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.

Answer: around 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

Are you studying on the go? Check out our FREE app and post questions on the fly!
Download on the
App Store
...
Apr 13th, 2015
...
Apr 13th, 2015
Dec 8th, 2016
check_circle
Mark as Final Answer
check_circle
Unmark as Final Answer
check_circle
Final Answer

Secure Information

Content will be erased after question is completed.

check_circle
Final Answer