A population of 100 individuals has a doubling time of 25 years. What size will this population be in 100 years?

Options

A. 100
B. 400
C. 1600
D. 3200

Answer

To solve the problem of determining the size of a population after a certain period given its doubling time, we can follow these steps:

### Step 1: Understand the Doubling Time
The doubling time of a population is the time it takes for the population to double in size. In this case, the population has a doubling time of 25 years.

### Step 2: Determine the Number of Doubling Periods
To find out how many times the population will double in 100 years, we can divide the total time period by the doubling time:
\[ \text{Number of Doublings} = \frac{\text{Total Time}}{\text{Doubling Time}} = \frac{100 \text{ years}}{25 \text{ years}} = 4 \]

### Step 3: Calculate the Population Size After Each Doubling
Starting with an initial population of 100 individuals, we can calculate the population size after each doubling:
1. After 1 doubling (25 years):
\[ 100 \times 2^1 = 200 \]
2. After 2 doublings (50 years):
\[ 100 \times 2^2 = 400 \]
3. After 3 doublings (75 years):
\[ 100 \times 2^3 = 800 \]
4. After 4 doublings (100 years):
\[ 100 \times 2^4 = 1600 \]

### Step 4: Final Population Size
After 100 years, the population size will be:
\[ \text{Final Population Size} = 1600 \]

### Conclusion
The size of the population after 100 years will be **1600 individuals**.

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