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An 80-gram sample of a radioactive substance decayed to 10 grams after 300 minutes. find the half-life of the substance

Guest May 23, 2017

#1**0 **

10 = 80 x 2^-(300/h), solve for h

Solve for h over the real numbers:

10 = 5 2^(4 - 300/h)

10 = 5 2^(4 - 300/h) is equivalent to 5 2^(4 - 300/h) = 10:

5 2^(4 - 300/h) = 10

Divide both sides by 5:

2^(4 - 300/h) = 2

Take reciporicals of both sides:

2^(300/h - 4) = 1/2

Take the logarithm base 2 of both sides:

300/h - 4 = -1

Bring 300/h - 4 together using the common denominator h:

-(4 (h - 75))/h = -1

Multiply both sides by h:

-4 (h - 75) = -h

Expand out terms of the left hand side:

300 - 4 h = -h

Subtract 300 - h from both sides:

-3 h = -300

Divide both sides by -3:

Answer: | h = 100 minutes - the half-life.

Guest May 23, 2017

#2**0 **

An 80-gram sample of a radioactive substance decayed to 10 grams after 300 minutes. find the half-life of the substance.

10 = 80*2^-(300/h), solve for h. Divide both sides by 80,

0.125 = 2^-(300/h) take the ln of both sides,

-2.0794415... =-(300/h)*0.6931472..... divide both sides by 0.6931472.....

-3 = -(300/h) cross multiply

-3h = -300 divide both sides by -3

h =-300/-3

h= 100 minutes - the half-life of the radioactive substance.

Guest May 23, 2017