(a)-A fossilised tree was tested and contains 10 grams of Carbon-14. Given that there was 12 grams of Carbon-14 present when it died, determine the age of the fossil? Half life of Carbon-14 is 5700 years.

Question

(b)How much Carbon-14 will be present in the sample 100 years from now?
Need easily understandable steps to get my head around.
Thanks in advance

Answer 1

For half-life questions, it is usual to use a base of 1/2 or .5
amount = 12 (1/2)^(t/5700) , where t is the number of years
if the amount = 10
10 = 12 (.5)^(t/5700)
.8333... = .5^(t/5700)
take logs of both sides and use log rules
log .8333... = (t/5700) log .5
t/5700 = log .8333... / log .5

see if you can get t = appr 1499 years

for your second part, evaluate
amount = 12 (.5)^(100/5700)

let me know what you got

in general, for half-life questions:
amount = a (.5)^(t/k)
where a is the starting amount, and k is the half-life time , t and k of the same units of time

For "doubling" type of questions, use a base of 2