When a sample of atoms is irradiated by neutrons, radioactive atoms are produced at a constant rate R, which decay with decay constant $$\lambda$$. The number of radioactive atoms accumulated after an irradiation time t is given by

A

$$N(t) = Rt\,e^{-\lambda t}$$

B

$$N(t) = \frac{R}{\lambda}e^{-\lambda t}$$

C

$$N(t) = \frac{R}{\lambda}\left(1 - e^{-\lambda t}\right)$$

D

$$N(t) = Rt\left(1 - e^{-\lambda t}\right)$$