A population of bacteria doubles every 3 hours. If you start with 500 bacteria, how many will there be after 9 hours?

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To determine the number of bacteria after 9 hours, let's break down the problem step by step.

### Given:
- **Initial Population ($$ P_0 $$)**: 500 bacteria
- **Doubling Time**: Every 3 hours
- **Total Time ($$ t $$)**: 9 hours

### Steps to Calculate:

1. **Determine the Number of Doubling Periods:**

Since the population doubles every 3 hours, and the total time is 9 hours:
   
   $$
   \text{Number of Doublings} = \frac{\text{Total Time}}{\text{Doubling Time}} = \frac{9 \text{ hours}}{3 \text{ hours/doubling}} = 3 \text{ doublings}
   $$

2. **Apply the Doubling Formula:**

The population after a certain number of doublings can be calculated using the formula:
   
   $$
   P = P_0 \times 2^n
   $$
   
   where:
   - $$ P $$ = final population
   - $$ P_0 $$ = initial population
   - $$ n $$ = number of doublings
   
   Plugging in the values:
   
   $$
   P = 500 \times 2^3 = 500 \times 8 = 4000
   $$

### **Conclusion:**
After 9 hours, the bacterial population will grow to **4,000 bacteria**.
After 9 hours, there will be 4,000 bacteria.

A population of bacteria doubles every 3 hours. If you start with 500 bacteria, how many will there be after 9 hours?

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