The population of amoebas in a colony doubles every two days. If there were 200 amoebas in the colony six days ago, how many amoebas will there be four days from now?

Answer

To solve the problem step by step, we will follow the reasoning presented in the video transcript.

### Step 1: Determine the total time period
We need to find out how many days will elapse from six days ago to four days from now.

**Calculation:**
- Days elapsed = 6 days (ago) + 4 days (from now) = 10 days

### Step 2: Calculate the number of doubling periods
The population of amoebas doubles every two days. To find out how many times the population will double in 10 days, we divide the total number of days by the doubling period.

**Calculation:**
- Number of doubling periods = Total days / Doubling period = 10 days / 2 days = 5 times

### Step 3: Calculate the final population
We started with 200 amoebas six days ago. Since the population doubles 5 times, we can express the final population using the formula:

**Calculation:**
- Final population = Initial population × (2^number of doublings)
- Final population = 200 × (2^5)

Now, we calculate \(2^5\):
- \(2^5 = 32\)

Now multiply:
- Final population = 200 × 32 = 6400

### Conclusion
The number of amoebas in the colony four days from now will be **6400**.

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