15-5 어떤 단세포 생물의 집단은 1 분마다 $30 \%$ 가 죽고, 나머지는 각각 두 마리로 분열한다고 한다. 처음 10 마리의 단세포 생물의 수가 처음으로 1000 마리 이상이 되는 것은 몇 분 후인가? 단, $1.4^{13}=79.4$ 로 계산한다.
Answer
\( \boxed{14} \) minutes are needed for the population of single-celled organisms to reach 1000 or more.
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.
