At $$ 10: 05 $$ a.m., there are 2 microscopic bacteria cells in the bottle. At $$ 10: 15 $$ a.m., there are 8 cells in the bottle. At what time will there be 16 cells in the bottle? At what time will there be 64 cells in the bottle? $$ 10: 30 $$ a.m.

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To determine the times at which the bacteria count reaches 16 and 64 cells, let's analyze the growth pattern:

1. **Initial Data:**
   - **10:05 a.m.**: 2 cells
   - **10:15 a.m.**: 8 cells

2. **Growth Analysis:**
   - From 10:05 to 10:15 (10 minutes), the number of cells increases from 2 to 8, which is a **4-fold increase**.
   - This suggests that the bacteria **double every 5 minutes**:
     - **First 5 minutes (10:05 to 10:10)**: 2 → 4 cells
     - **Next 5 minutes (10:10 to 10:15)**: 4 → 8 cells

3. **Predicting Future Growth:**
   - **To reach 16 cells:**
     - Next 5 minutes (10:15 to 10:20): 8 → 16 cells
   - **To reach 64 cells:**
     - Continuing to double every 5 minutes:
       - 10:20 → 20:25: 16 → 32 cells
       - 10:25 → 10:30: 32 → 64 cells

4. **Conclusion:**
   - **16 cells** will be present at **10:20 a.m.**
   - **64 cells** will be present at **10:30 a.m.**

**Answer:**
- There will be 16 cells at 10:20 a.m.
- There will be 64 cells at 10:30 a.m.
There will be 16 cells at 10:20 a.m. and 64 cells at 10:30 a.m.

At \( 10: 05 \) a.m., there are 2 microscopic bacteria cells in the bottle. At \( 10: 15 \) a.m., there are 8 cells in the bottle. At what time will there be 16 cells in the bottle? At what time will there be 64 cells in the bottle? \( 10: 30 \) a.m.

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