A population of bacteria doubles every 2 hours . What is the percent increase after 4 hours ?

Options

A. 400
B. 500
C. 300
D. 600

Answer

To solve the problem of finding the percent increase in a population of bacteria that doubles every 2 hours after 4 hours, we can follow these steps:

### Step-by-Step Solution:

1. **Initial Population**: Let's denote the initial population of bacteria at time \( t = 0 \) as \( x \).

2. **Population After 2 Hours**: Since the population doubles every 2 hours, after 2 hours, the population will be:
\[ \text{Population after 2 hours} = 2x \]

3. **Population After 4 Hours**: After another 2 hours (which makes a total of 4 hours), the population will again double:
\[ \text{Population after 4 hours} = 2 \times (2x) = 4x \]

4. **Calculating the Increase in Population**: The increase in population after 4 hours compared to the initial population is:
\[ \text{Increase} = \text{Population after 4 hours} - \text{Initial Population} = 4x - x = 3x \]

5. **Calculating Percent Increase**: The percent increase is calculated using the formula:
\[ \text{Percent Increase} = \left( \frac{\text{Increase}}{\text{Initial Population}} \right) \times 100 \]
Substituting the values we have:
\[ \text{Percent Increase} = \left( \frac{3x}{x} \right) \times 100 = 3 \times 100 = 300\% \]

### Final Answer:
The percent increase in the population of bacteria after 4 hours is **300%**.