https://file.aiquickdraw.com/mathbot/file/1727353642637g5n1u35o.jpg

The example from your image discusses the varying world population growth rates and asks for the approximate doubling times for different rates. Here's how we can approach this problem:

### Key Information:
1. **Average growth rate**: 0.7%
2. **Peaked growth rate in the 1960s**: 2.1%
3. **Current (2013) growth rate**: 1.1%
4. **2013 population**: 7.1 billion
5. **Year for prediction**: 2050

### Formula to Use: Doubling Time
To calculate the doubling time, we use the **Rule of 70**, which is a common approximation in population studies:

\[
\text{Doubling Time} \approx \frac{70}{\text{Growth Rate (in %)}}
\]

### Calculating Doubling Time for Each Rate:
1. **For 0.7% growth rate**:
   \[
   \text{Doubling Time} \approx \frac{70}{0.7} = 100 \, \text{years}
   \]
   
2. **For 2.1% growth rate**:
   \[
   \text{Doubling Time} \approx \frac{70}{2.1} \approx 33.33 \, \text{years}
   \]
   
3. **For 1.1% growth rate**:
   \[
   \text{Doubling Time} \approx \frac{70}{1.1} \approx 63.64 \, \text{years}
   \]

### Predicting the Population in 2050
To predict the world population for 2050 based on the given growth rates, we need to calculate how many doublings could happen between 2013 and 2050.

1. **Time between 2013 and 2050**: 
   \[
   2050 - 2013 = 37 \, \text{years}
   \]
   
2. **For 0.7% growth rate**: 
   Using 100 years as the doubling time, less than half of a doubling will happen by 2050. So the population would not double by then and would be slightly higher than 7.1 billion.

3. **For 2.1% growth rate**: 
   Using 33.33 years as the doubling time, a little more than one doubling could happen by 2050. This means the population would approximately double from 7.1 billion to around 14.2 billion.

4. **For 1.1% growth rate**: 
   Using 63.64 years as the doubling time, less than one doubling would happen by 2050. The population would be somewhat higher but still less than double 7.1 billion.

Would you like more details on any of these calculations?

---

### Related Questions:
1. What is the exact population growth rate required to double the population in 50 years?
2. How do other factors like migration or birth rates impact real-world population growth?
3. What other mathematical models can be used to predict population growth more accurately than the Rule of 70?
4. How would a declining growth rate affect future population estimates?
5. How does the exponential nature of population growth influence resources and environmental sustainability?

### Tip:
The Rule of 70 provides a quick estimate, but remember that it assumes constant growth, which is often not realistic in complex systems like global population. Always check for changes in growth rates over time.

Find the approximate doubling time for different growth rates and predict the world population in 2050 based on a 2013 population of 7.1 billion.

Learn how to calculate the doubling time using the Rule of 70 and predict the world population for 2050 based on varying growth rates. This example covers key concepts such as exponential growth and population growth, suitable for high school students in Grades 9-12.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation