Consider a population of 10 million cells. Given the per-capita...

Given initial population $N_0 = 10$ million.

Per-capita birth rate $b = 0.002$.

Per-capita death rate $d = 0.002$.

The intrinsic rate of natural increase $r$ is given by $r = b - d$.

$r = 0.002 - 0.002 = 0$.

The population growth equation is $N_t = N_0 e^{rt}$.

Substituting $r = 0$, we get $N_t = N_0 e^0 = N_0$.

Thus, the population size remains constant over time.

The expected number of cells after $10$ generations is $10$ million.

Answer: $10$ million