16. The world population in 1975 was approximately 4 billion, and was determined to be growing exponentially at a rate of 1.9 % per year. If the formula for population growth is given as f(x) = 4e⁰019t calculate the world population expected in 2015.
16. The world population in 1975 was approximately 4 billion, and was determined to be growing exponentially at a rate of 1.9 % per year. If the formula for population growth is given as f(x) = 4e⁰019t calculate the world population expected in 2015.
Algebra and Trigonometry (6th Edition)
6th Edition
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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![### Population Growth Calculation Example
**Problem Statement:**
The world population in 1975 was approximately 4 billion and was determined to be growing exponentially at a rate of 1.9% per year. Given the formula for population growth is:
\[ f(x) = 4e^{0.019t} \]
Calculate the world population expected in 2015.
### Explanation:
1. **Understanding the Given Data:**
- **Initial Population (1975):** 4 billion
- **Growth Rate:** 1.9% per year
- **Formula:** \( f(x) = 4e^{0.019t} \)
2. **Variables:**
- \( t \) represents the time in years since 1975.
- You need to find the population in 2015.
3. **Calculation Steps:**
- Find the value of \( t \) for the year 2015:
\[ t = 2015 - 1975 = 40 \]
- Plug \( t = 40 \) into the population growth formula:
\[ f(x) = 4e^{0.019 \times 40} \]
- Simplify the exponent:
\[ 0.019 \times 40 = 0.76 \]
- Therefore, the formula becomes:
\[ f(x) = 4e^{0.76} \]
- Using a calculator to find the value of \( e^{0.76} \):
\[ e^{0.76} \approx 2.138 \]
- Multiply by the initial population (4 billion):
\[ f(x) = 4 \times 2.138 \approx 8.552 \]
4. **Conclusion:**
- The world population expected in 2015, according to this model, is approximately **8.552 billion**.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F9168bf64-9e72-49b9-9a77-a0f13a9541a3%2Faf9549cd-91f6-4bfd-a51c-071aa90c5429%2Fl62ehyn_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Population Growth Calculation Example
**Problem Statement:**
The world population in 1975 was approximately 4 billion and was determined to be growing exponentially at a rate of 1.9% per year. Given the formula for population growth is:
\[ f(x) = 4e^{0.019t} \]
Calculate the world population expected in 2015.
### Explanation:
1. **Understanding the Given Data:**
- **Initial Population (1975):** 4 billion
- **Growth Rate:** 1.9% per year
- **Formula:** \( f(x) = 4e^{0.019t} \)
2. **Variables:**
- \( t \) represents the time in years since 1975.
- You need to find the population in 2015.
3. **Calculation Steps:**
- Find the value of \( t \) for the year 2015:
\[ t = 2015 - 1975 = 40 \]
- Plug \( t = 40 \) into the population growth formula:
\[ f(x) = 4e^{0.019 \times 40} \]
- Simplify the exponent:
\[ 0.019 \times 40 = 0.76 \]
- Therefore, the formula becomes:
\[ f(x) = 4e^{0.76} \]
- Using a calculator to find the value of \( e^{0.76} \):
\[ e^{0.76} \approx 2.138 \]
- Multiply by the initial population (4 billion):
\[ f(x) = 4 \times 2.138 \approx 8.552 \]
4. **Conclusion:**
- The world population expected in 2015, according to this model, is approximately **8.552 billion**.
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