題目
Problem
甲、填充題:共 8 題,每題 8 分,共 64 分。請將答案依題號順序寫在答案卷上,不必寫演算過程。
- A new drug is introduced through an advertising campaign to a population of 1 million potential customers. The rate at which the population hears about the drug is assumed to be proportional to the number of people who are not yet aware of the drug. By the end of 1 year, half of the population has heard of the drug. How many will have heard of it by the end of 2 years? Answer : \underline{\quad(1)\quad}
解答
解法一
思路
展開
令 為已得知的人數。尚未得知的人數 決定增加速率,故建立飽和型的一階微分方程。
答題過程
展開
設 。由
得
已知 ,所以 。因此