5. The radioactive decay of a substance is given by
$$R = 1000 \mathrm { e } ^ { - c t } , \quad t \geqslant 0 .$$
where \(R\) is the number of atoms at time \(t\) years and \(c\) is a positive constant.
- Find the number of atoms when the substance started to decay.
It takes 5730 years for half of the substance to decay.
- Find the value of \(c\) to 3 significant figures.
- Calculate the number of atoms that will be left when \(t = 22920\).
- In the space provided on page 13, sketch the graph of \(R\) against \(t\).