The half-life of a radioactive substance is the time required for half of a sample to undergo radioactive decay, or for the quantity to fall to half its original amount. carbon 14 has a half-life of 5,730 years. suppose given samples of carbon 14 weigh (fraction 5/8) of a pound and (fraction 7/8) of a pound. what was the total weight of the samples 11460 years ago
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Amount of C-14 taken were 2.5 pounds and 3.5 pounds respectively.

Step-by-step explanation:

Radioactive decay is an exponential process represented by

where = Amount of the radioactive element after t years

= Initial amount

k = Decay constant

t = time in years

Half life period of Carbon-14 is 5730 years.

Now we take ln (Natural log) on both the sides

-ln(2) = -5730kln(e)

0.69315 = 5730k

Now we have to calculate the weight of samples of C-14 taken for the remaining quantities and of a pound.

pounds

Similarly for pounds

pounds

a) y = -3x +2

b) y = 1/2x -6

these 2 can be combined into one equation.

-3x +2 = .5x -6

8 = 3.5x

x = 8 / 3.5 = 2.2857142857

y = -3 * (8 / 3.5) +2

y = (-24 / 3.5) + 2

y = -4.8571428571

step-by-step explanation: