Carbon dating is a tool used to determine the age of a fossil. For example, a humanoid skull was found in a cave along with the remains of a campfire. Archaeologists believe the age of the skull to be the same as the campfire. Assume that the rate of decay of a radioactive substance is proportional to the amount of the substance present. The half-life of a radioactive substance is the time it takes to reduce to half its initial amount. (a) Write an initial-value problem that models the amount of carbon-14 in the campfire. (b) If it is determined that only 2% of the original amount of carbon-14 remains in the burnt wood of the campfire, find an explicit solution to the initial-value problem from part (a). Use the solution to estimate the age of the skull if the half-life of carbon-14 is about 5700 years.

Question

Carbon dating is a tool used to determine the age of a fossil. For example, a humanoid skull was found in a cave
along with the remains of a campfire. Archaeologists believe the age of the skull to be the same as the campfire.
Assume that the rate of decay of a radioactive substance is proportional to the amount of the substance present. The
half-life of a radioactive substance is the time it takes to reduce to half its initial amount.

for part a I beleive that this is y'=ky where y is the amount of C₁₄ and y(o) = y₀ but I am probably wrong.

for part b I have no clue how to do this.