**Exponential Population Growth Analysis** The exponential function \( N = 5000 \times 1.73^d \), where \( d \) is measured in decades, provides the number of individuals in a specified population. All answers are rounded as instructed. **(a) Calculate \( N(1.6) \):** Given: \[ N(1.6) = 5000 \times 1.73^{1.6} \approx 12018.32 \] Explanation: The population is about 12,018.32 people after 16 years. --- **(b) What is the percentage growth rate per decade?** Calculation: \[ 5000 \times 1.73^1 = 8650 \] \[ 8650 - 5000 = 3650 \] \[ \frac{3650}{5000} = 0.73 \] The percentage growth rate per decade is approximately 73%. --- **(c) What is the yearly growth factor rounded to three decimal places?** Calculation: \[ 1.73^{1/10} \approx 1.056 \] The yearly growth factor is approximately 1.056. **What is the yearly percentage growth rate?** Calculation: The yearly percentage growth rate is approximately 5.6%. --- **(d) What is the growth factor for a century?** Calculation: \[ 1.73^{10} \approx 240.138 \] The growth factor for a century is approximately 240.138. **What is the percentage growth rate per century?** Calculation: The percentage growth rate per century is approximately 24013.8%.
**Exponential Population Growth Analysis** The exponential function \( N = 5000 \times 1.73^d \), where \( d \) is measured in decades, provides the number of individuals in a specified population. All answers are rounded as instructed. **(a) Calculate \( N(1.6) \):** Given: \[ N(1.6) = 5000 \times 1.73^{1.6} \approx 12018.32 \] Explanation: The population is about 12,018.32 people after 16 years. --- **(b) What is the percentage growth rate per decade?** Calculation: \[ 5000 \times 1.73^1 = 8650 \] \[ 8650 - 5000 = 3650 \] \[ \frac{3650}{5000} = 0.73 \] The percentage growth rate per decade is approximately 73%. --- **(c) What is the yearly growth factor rounded to three decimal places?** Calculation: \[ 1.73^{1/10} \approx 1.056 \] The yearly growth factor is approximately 1.056. **What is the yearly percentage growth rate?** Calculation: The yearly percentage growth rate is approximately 5.6%. --- **(d) What is the growth factor for a century?** Calculation: \[ 1.73^{10} \approx 240.138 \] The growth factor for a century is approximately 240.138. **What is the percentage growth rate per century?** Calculation: The percentage growth rate per century is approximately 24013.8%.
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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![**Exponential Population Growth Analysis**
The exponential function \( N = 5000 \times 1.73^d \), where \( d \) is measured in decades, provides the number of individuals in a specified population. All answers are rounded as instructed.
**(a) Calculate \( N(1.6) \):**
Given:
\[ N(1.6) = 5000 \times 1.73^{1.6} \approx 12018.32 \]
Explanation:
The population is about 12,018.32 people after 16 years.
---
**(b) What is the percentage growth rate per decade?**
Calculation:
\[ 5000 \times 1.73^1 = 8650 \]
\[ 8650 - 5000 = 3650 \]
\[ \frac{3650}{5000} = 0.73 \]
The percentage growth rate per decade is approximately 73%.
---
**(c) What is the yearly growth factor rounded to three decimal places?**
Calculation:
\[ 1.73^{1/10} \approx 1.056 \]
The yearly growth factor is approximately 1.056.
**What is the yearly percentage growth rate?**
Calculation:
The yearly percentage growth rate is approximately 5.6%.
---
**(d) What is the growth factor for a century?**
Calculation:
\[ 1.73^{10} \approx 240.138 \]
The growth factor for a century is approximately 240.138.
**What is the percentage growth rate per century?**
Calculation:
The percentage growth rate per century is approximately 24013.8%.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fc49c9615-4f22-4f84-a617-639a09f12ba4%2Fc4b2011f-b6b8-48b1-8716-e1091905dc05%2Flomlh96.jpeg&w=3840&q=75)
Transcribed Image Text:**Exponential Population Growth Analysis**
The exponential function \( N = 5000 \times 1.73^d \), where \( d \) is measured in decades, provides the number of individuals in a specified population. All answers are rounded as instructed.
**(a) Calculate \( N(1.6) \):**
Given:
\[ N(1.6) = 5000 \times 1.73^{1.6} \approx 12018.32 \]
Explanation:
The population is about 12,018.32 people after 16 years.
---
**(b) What is the percentage growth rate per decade?**
Calculation:
\[ 5000 \times 1.73^1 = 8650 \]
\[ 8650 - 5000 = 3650 \]
\[ \frac{3650}{5000} = 0.73 \]
The percentage growth rate per decade is approximately 73%.
---
**(c) What is the yearly growth factor rounded to three decimal places?**
Calculation:
\[ 1.73^{1/10} \approx 1.056 \]
The yearly growth factor is approximately 1.056.
**What is the yearly percentage growth rate?**
Calculation:
The yearly percentage growth rate is approximately 5.6%.
---
**(d) What is the growth factor for a century?**
Calculation:
\[ 1.73^{10} \approx 240.138 \]
The growth factor for a century is approximately 240.138.
**What is the percentage growth rate per century?**
Calculation:
The percentage growth rate per century is approximately 24013.8%.
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