The bacteria in a culture grows by 10% in the first hour, decreases by 10% in the second hour and again increases by 10% in the third hour. Find the bacteria at the end of 3 hours if the count was initially 20000.

Options

A. `20967`
B. `21000`
C. `28890`
D. `21780`

Answer

To solve the problem step by step, we will calculate the growth and decrease of bacteria at each hour based on the given percentages.

### Step 1: Initial Count of Bacteria
The initial count of bacteria is given as 20,000.

### Step 2: Calculate the Count After the First Hour
The bacteria grows by 10% in the first hour. To calculate the new count:
- Increase = 10% of 20,000 = (10/100) * 20,000 = 2,000
- New Count = Initial Count + Increase = 20,000 + 2,000 = 22,000

### Step 3: Calculate the Count After the Second Hour
In the second hour, the bacteria decreases by 10%. We will calculate the decrease based on the count after the first hour (22,000):
- Decrease = 10% of 22,000 = (10/100) * 22,000 = 2,200
- New Count = Previous Count - Decrease = 22,000 - 2,200 = 19,800

### Step 4: Calculate the Count After the Third Hour
In the third hour, the bacteria again increases by 10%. We will calculate the increase based on the count after the second hour (19,800):
- Increase = 10% of 19,800 = (10/100) * 19,800 = 1,980
- New Count = Previous Count + Increase = 19,800 + 1,980 = 21,780

### Final Count
The final count of bacteria after 3 hours is **21,780**.

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