Question

In 1947 a large collection of papyrus scrolls, including the oldest known manuscript version of the Old Testament, was found in a cave near the Dead Sea; they have come to be known as the “Dead Sea Scrolls”. The scroll containing the book of Isaiah was dated in 1994 using the radiocarbon technique and it was found to contain between 75% to 77% of the initial level of carbon 14. Radioactive decay is modeled by the function

m (t) = m₀ e^-kt

where m₀ is the initial mass of a radioactive substance, k is the relative decay rate and t is time.

(a) Show that if the half-life of carbon 14 is 5700 years then k ≈ 1.216 × 10^-4. Half-life is the time it takes for half of the radioactive isotopes to decay.

(b) Between which dates was the scroll written?

(c) If the scroll will be dated today how much carbon 14 will it contain (as a percentage of the initial level)?

write neatly and show all of the steps in an organized way.

Answer 1

CSAo6) , 216x10 co bonz)コs- -_-/. After 2365-Btear s So, g.3b55 38

(c- Todaブ→ 201g. -£1.21 6 X 1 O-4) (2:1-38) 1-2, 6 tio") (2350-3) So,co be daled o da