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5Question: In a distant galaxy, a space station orbits a planet every $ \frac{5\pi}{2} $ hours. How many whole hours are in the interval between two consecutive orbits?
Solution: The time between two consecutive orbits is $ \frac{5\pi}{2} $ hours. Since $ \pi \approx 3.1416 $, we compute:
\frac{5 \times 3.1416}{2} = \frac{15.708}{2} = 7.854
The interval contains all whole numbers from 1 up to 7, because 7.854 is less than 8.
Thus, the whole numbers in the interval are $ 1, 2, 3, 4, 5, 6, 7 $.
There are $ 7 $ whole numbers.
Question: An ornithologist observes a flock of birds migrating, where the number of birds doubles every day starting from 3 birds on day one. On what day does the total count first exceed 500 birds?