A -gram sample of carbon-14 decays over time so that its mass (in grams) satisfies
MATHEMATICS · Multi-part · A Level · Mathematics · Exponentials and logarithms · Exponentials and logarithms
Problem
A 1.000-gram sample of carbon-14 decays over time so that its mass M(t) (in grams) satisfies dtdM=kM, where t is measured in years and k<0. After 2000 years, the mass has decreased to 0.785 g.
(a) Determine the exact value of the decay constant k (in yr−1). Express your answer as a natural logarithm.
(b) Compute the half-life of carbon-14, accurate to the nearest year.
(c) Predict the amount of carbon-14 remaining after 10000 years. Round your answer to three decimal places.