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Total time: 25 + 40 + 30 = 95 minutes
#### 95Certainly! Below are five math problems inspired by marine ecology, coral reef conservation, and coral genetic restoration research, each followed by a detailed solution. As requested, the questions are more difficult and tailored to advanced high school or early university level.
This is exponential growth. The general solution is:
where $n = 120$, $k = 18$, $p = 0.15$.
We approximate using the normal distribution due to large $n$, but for accuracy, use Poisson approximation or direct computation. Alternatively, use known binomial formula or calculator:
Using statistical software or approximation, the value is approximately:
However, drones cover circular area:
Since drones cannot be fractional and must cover fully, round up:
This is a linear recurrence. The general solution is:
Solve for constant using $p_0 = 0.3$:
