An isotope decays at a rate of -0.0049% per year. Find the half life. (show the work)

  14,146 years

Step-by-step explanation:

The annual multiplier is (1 -0.0049%) = 0.999951. We want to find the number of times this needs to be multiplied to make the product 1/2.

  0.5 = 0.999951^t

  log(0.5) = t·log(0.999951)

  log(0.5)/log(0.999951) = t ≈ 14,145.514

The half-life is about 14,146 years.

none of the above.

for one of the equations to be used in the process, there has to be a term in the equation since squared is .

since there is only a term in the first equation, we cannot derive a from completing the square.

solving with completing the square

set each factor equal to 0

4x-3 = 0

2x-1 = 0

solve for x.

4x-3=0

4x=3

x= 3/4

solve for x. 

2x-1= 0

2x= 1

x= 1/2

eventually after a few more steps, your answer should be 1/2 is less than or equal to x and 3/4 is greater than or equal to x