Question

Zhang lei tracked the size of the bear population in a nature reserve. the first year, there were [1000] bears. sadly, the population lost [10%] of its size each year. let [f(n)] be the number of bears in the reserve in the [n^text{th}] year since zhang lei started tracking it. [f] is a sequence. what kind of sequence is it?

(a) Arithmetic sequence
(b) Geometric sequence
(c) Exponential sequence
(d) Fibonacci sequence

Answer 1

The sequence described by Zhang Lei tracking the bear population, which decreases by a constant percentage each year, is a geometric sequence.

Step-by-step explanation:

The sequence described is f(n) which represents the number of bears in the nature reserve in the nth year. Since the bear population decreases by a constant percentage (10%) each year, this is a characteristic of a geometric sequence. An arithmetic sequence would have a constant difference between consecutive terms, which is not the case here. Instead, each year's population is 90% (or 0.9 times) of the previous year's population - a classic example of a geometric sequence.

Here's how the sequence behaves:
Year 1: 1000 bears
Year 2: 1000 x 0.9 = 900 bears
Year 3: 900 x 0.9 = 810 bears
And so on...

This pattern is clearly not linear (arithmetic), does not follow the specific pattern of adding the two previous numbers to get the next (Fibonacci), nor is it an exponential sequence where the rate of growth is proportional to the current amount and can increase or decrease at an ever-changing rate. A geometric sequence fits perfectly because each term is a constant multiple of the term before.