Step 1 :Given the initial population P(0) = 10, and the growth rule P(t+1) = 2 * (1 - 0.3) * P(t), we need to find the smallest integer t such that P(t) >= 1000.
Step 2 :Using the given value of $1.4^{13} = 79.4$, we can calculate the population at time t as P(t) = 10 * $1.4^t$.
Step 3 :We need to find the smallest integer t such that 10 * $1.4^t$ >= 1000.
Step 4 :By trial and error, we find that t = 14 gives a population of 10 * $1.4^{14}$ = 1111.2, which is greater than 1000.
Step 5 :\( \boxed{14} \) minutes are needed for the population of single-celled organisms to reach 1000 or more.