You're right to question it — let's **recheck** everything carefully and provide a plain, correct explanation.
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### **Question Recap:**
A scientist will destroy a bacteria sample **4 hours from now**, **immediately after a doubling**.
You are asked:
> **How many cells will the population contain at that time?**
We are given two **statements**.
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## ✅ **Statement (1):**
> The population just divided and, since the population divided two hours ago, the population has quadrupled, increasing by 3,750 cells.
### Step-by-step:
* The bacteria **just divided** now (time = 0).
* It **also divided 2 hours ago**, so doubling happens **every 2 hours**.
* Between 2 hours ago and now, the population **quadrupled**.
* This is **2 doublings**: $P \rightarrow 2P \rightarrow 4P$
* The population increased by **3,750 cells** in that time.
Let’s solve for the initial population 2 hours ago:
$$
4x - x = 3750 \Rightarrow 3x = 3750 \Rightarrow x = 1250
$$
So:
* 2 hours ago: 1250 cells
* Now: $4 \times 1250 = 5000$ cells
We know the doubling interval = **2 hours**, and:
* 2 hours from now: 10,000
* 4 hours from now: 20,000
✅ **We can calculate the population 4 hours from now: 20,000 cells.**
👉 **Statement (1) is sufficient.**
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## ❌ **Statement (2):**
> The population will double to 40,000 cells with one hour remaining until the scientist destroys the sample.
Let’s analyze:
* The destruction happens in **4 hours**.
* So this doubling (to 40,000) occurs at **3 hours from now**.
* That means **just before 3 hours**, the population was **20,000**.
* But we **don’t know the doubling interval** — it could be:
* Every 1 hour (20,000 → 40,000 at 3hr → 80,000 at 4hr), or
* Every 3 hours (no doubling at 4hr), or
* Any other value.
We don't know:
* **How many times** the population will double between now and 4 hours from now.
* Therefore, we **can’t calculate** the final population.
❌ **Statement (2) is not sufficient.**
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### ✅ **Final Answer: A**
> **Statement (1) alone is sufficient, but statement (2) alone is not sufficient.**
Let me know if you'd like a general approach for these kinds of exponential-growth problems!
mun23
A scientist is studying bacteria whose cell population doubles at constant intervals, at which times each cell in the population divides simultaneously. Four hours from now, immediately after the population doubles, the scientist will destroy the entire sample. How many cells will the population contain when the bacteria is destroyed?
(1) The population just divided and, since the population divided two hours ago, the population has quadrupled, increasing by 3,750 cells.
(2) The population will double to 40,000 cells with one hour remaining until the scientist destroys the sample