A factory produces a radioactive substance A at a constant rate R which decays with a decay constant ` lambda` to form a stable substance. Find (a) the number of nuclei of A and (b) number of nuclei of B, at any time t assuming the production of A starts at `t=0`. (c ) Also, find out the maximum number of nuclei of `A` present at any time during its formation.

Explanation

To solve the problem step by step, we will derive the number of nuclei of the radioactive substance A and the stable substance B, as well as the maximum number of nuclei of A present at any time during its formation.

### Step 1: Define the variables and the differential equation
Let:
- \( R \) = rate of production of substance A (constant)
- \( \lambda \) = decay constant of substance A
- \( n_A(t) \) = number of nuclei of substance A at time \( t \)
- \( n_B(t) \) = number of nuclei of substance B at time \( t \)
...