If a tree dies and the trunk remains undisturbed for 1.360 × 10⁴ years, what percentage of the original ¹⁴C is still present? (The half-life of ¹⁴C is 5730 years.)

Question

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If a tree dies and the trunk remains undisturbed for 1.360 × 10⁴ years, what percentage of the original ¹⁴C is still present? (The half-life of ¹⁴C is 5730 years.)

Answer 1

In order to find the exact amount remaining you will neN9ted to use the equation:

N(t)=N(0) (1/2)^t/t/12

N(t)= the amount remaining after the given amount of time

N(0)= the starting amount (in this case we will put it as 100 because we are using percentages)

t= the amount of time that has passed

t1/2= the half life

N(t)=100(1/2)^(1.36E4/5730)

= 19.298%

Answer 2

Make the chart number half lives / time / %. You need to start at time zero and zero half lives then go up in number of half lives. Each half life is 5,730 years you can change that into scientific notation or change the time 1.360x10^4 into standard notation to help match up the times. Move the decimal to the right for std notation and count how many times you move it for sci notation.

you will need 3 half lives to get to that time 1.360 x10^4 so that means you need to reduce the % in half 3 times 100 > 50 > 25 > 12.5