Friday

April 25, 2014

April 25, 2014

Posted by **ronnieday** on Monday, March 19, 2012 at 12:43pm.

a) If a 100-gram sample of the radioactive substance decays to 95 grams after 1 year, find an equation that can model the mass of the of the sample after t years.

b) Find the mass of the sample after 50 years.

c) The half-life of a substance is the amount of time it takes for a sample to decay to half its original size. Find the half-life of the radioactive substance.

- calculus -
**Reiny**, Monday, March 19, 2012 at 1:17pmlet the equation be

A = 100 e^(kt)

a) if amount = 95

95 = 100 e^(1k)

.95 = e^k

k = ln .95

so A = 100 e^(ln.95 t)

when t = 50

A = 100 e^(50ln.95) = 7.69 g are left

for half-life time, only 50 g of the original 100g would remain

50 = 100 e^(ln.95 t)

.5 = e^(ln.95 t)

ln.95t = ln.5

t = ln.5/ln.95 = appr13.5 years

**Related Questions**

Math - D.E.Q. - The half-life of a radioactive isotope is the amount of time it ...

advanced functions HELP!!! - Radioactive decay is the process by which an ...

Differential Equations - Model radioactive decay using the notation t = time (...

ap calculus - suppose that the amount in grams of a radioactive substance ...

calculus - Carbon-14 is a radioactive substance produced in the Earth's ...

Science - Radioactive substance decays so that after t years, the amount ...

Calculus - The amount A in grams of radioactive plutonium remaining in a 20-gram...

Science- Radioactive Dating - Which of the following statements about ...

Calculus - The half-life of radioactive strontium-90 is approximately 31 years. ...

Calculus - The radioactive element polonium decays according to the law given ...