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Explanation & Answer
This is the formal final answer.
2. 𝑓(𝑥) = 200(2.5)𝑥 where 𝑥 is a 3-hour time period.
(a) This means that the population grows 2.5 times in 3 hours.
We need to find how many times it grows during 1 hour.
1
It is obviously 2.5(3) = √𝟐. 𝟓 ≈ 𝟏. 𝟑𝟔 (use exact or approximate value).
𝟑
(b) The corresponding model is 𝑔(𝑥) = 𝟐𝟎𝟎(𝟏. 𝟑𝟔)𝒙 (if we use approximate value).
The initial population (for 𝑥 = 0) is the same so we use the same factor of 200.
3. 𝑓(𝑥) = 200(0.45)𝑥 where 𝑥 is a 40-minute time period.
(a) The population decays by 0.45 in 40 minutes.
60
𝟑
This means it decays (0.45)(40) = (𝟎. 𝟒𝟓)(𝟐) �...