Algebra exponential decay problem

Question

Note that after 5715 years a given amount of carbon-14 will have decayed to half the original amount.

a. Find the exponential decay model for carbon-14. Round decay constant to 6 decimal places.

b. In 1947, earthenware jars containing what are known as the Dead Sea Scrolls were found by an Arab Bedouin herdsman. Analysis indicated that the scroll wrapping contained 76% of their original carbon-14. Estimate the age of Dead Sea Scrolls. Round your answer to a whole number.

Answer 1

a.

A = a₀(0.5)^t/5715

b.

0.76 = (0.5)^t/5715

ln 0.76 = (t / 5715)(ln 0.5)

Can you solve for t and answer?