(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.

(b)How much Carbon-14 will be present in the sample 150 years from now?

(a)(12 - 10) / 12 = (1/2)^(t / 5700)

log(1/6) = (t / 5700) log(1/2)

(b) (10 - c) / 10 = (1/2)^(150 / 5700)

To determine the age of the fossil, we can use the concept of half-life of Carbon-14. The half-life of Carbon-14 is 5700 years, which means that after every 5700 years, half of the Carbon-14 in a sample will decay.

(a) To find the age of the fossil, we need to calculate the number of half-lives that have occurred since it died.

1. First, calculate the fraction of Carbon-14 that remains in the fossil.
Fraction remaining = (Amount of Carbon-14 at present / Original amount of Carbon-14)
= (10 grams / 12 grams)
= 5/6

2. Next, calculate the number of half-lives using the formula:
Number of half-lives = (ln(remaining fraction) / ln(0.5))
= (ln(5/6) / ln(0.5))

3. Calculate the age of the fossil by multiplying the number of half-lives by the half-life of Carbon-14:
Age = (Number of half-lives * Half-life of Carbon-14)
= (ln(5/6) / ln(0.5)) * 5700 years

(b) To determine the amount of Carbon-14 that will be present in the sample 150 years from now, we can repeat the same steps but consider the remaining time as 150 years instead of the age.

1. Calculate the fraction of Carbon-14 that remains in the sample after 150 years.
Fraction remaining = (1/2)^(Time elapsed / Half-life of Carbon-14)
= (1/2)^(150 years / 5700 years)

2. Calculate the amount of Carbon-14 by multiplying the original amount by the remaining fraction:
Amount of Carbon-14 = (Original amount * Remaining fraction)
= (12 grams * (1/2)^(150 years / 5700 years))

By plugging in the values, you can find the exact age of the fossil and the amount of Carbon-14 that will remain after 150 years.