- [Maximum mark: 6]
Radioactive carbon is a material that decays over time.
The mass, m(t) (in nanograms), of radioactive carbon in a fossil of a plant, after t years, can be modelled by the function
m(t) = 120e⁻⁰·⁰⁰⁰¹²¹ᵗ
where t is the time since the plant died.
(a) Write down the initial mass of the radioactive carbon. [1]
(b) Find the mass of the radioactive carbon after 20 000 years. [2]
(c) Calculate the smallest number of complete years it takes for more than half the sample to decay. [3]