Calculating the Population Growth Rate

Oct 13, 2025 by miodeya.com 44 views

Introduction

In this article, we will explore the concept of population growth in a bird enclosure at a zoo. The initial population of birds in the enclosure is 350, and it is expected to increase by 5% every year. We will examine the function that accurately describes the population of birds in the enclosure over time.

Population Growth Formula

The population growth formula is given by:

P(t) = P0 * (1 + r)^t

where:

P(t) is the population at time t
P0 is the initial population
r is the rate of growth (in decimal form)
t is the time in years

Calculating the Population Growth Rate

The rate of growth is given as 5% per year. To convert this to a decimal, we divide by 100:

r = 5/100 = 0.05

Determining the Function that Accurately Describes the Population

We are given that the initial population of birds in the enclosure is 350. We can substitute this value into the population growth formula:

P(t) = 350 * (1 + 0.05)^t

Simplifying the formula, we get:

P(t) = 350 * (1.05)^t

This is the function that accurately describes the population of birds in the enclosure over time.

Example Calculations

Let's calculate the population of birds in the enclosure for a few different time periods:

After 1 year: P(1) = 350 * (1.05)^1 = 367.5
After 2 years: P(2) = 350 * (1.05)^2 = 386.225
After 3 years: P(3) = 350 * (1.05)^3 = 405.59375

Conclusion

In this article, we have explored the concept of population growth in a bird enclosure at a zoo. We have determined that the function that accurately describes the population of birds in the enclosure over time is given by:

P(t) = 350 * (1.05)^t

This function can be used to calculate the population of birds in the enclosure for any given time period.

Understanding the Exponential Growth Model

The population growth formula is an example of an exponential growth model. In this model, the population grows at a constant rate over time. The exponential growth model is often used to describe population growth in a variety of contexts, including biology, economics, and finance.

Key Features of the Exponential Growth Model

The exponential growth model has several key features that make it useful for describing population growth:

Constant rate of growth: The rate of growth is constant over time, which means that the population grows at a steady rate.
Exponential growth: The population grows exponentially, which means that the population grows faster and faster over time.
Initial population: The initial population is the starting point for the population growth model.
Time: The time variable represents the number of time periods over which the population grows.

Real-World Applications of the Exponential Growth Model

The exponential growth model has a wide range of real-world applications, including:

Population growth: The exponential growth model is often used to describe population growth in a variety of contexts, including biology, economics, and finance.
Epidemiology: The exponential growth model is used to describe the spread of diseases and the growth of populations.
Finance: The exponential growth model is used to describe the growth of investments and the value of assets over time.
Environmental science: The exponential growth model is used to describe the growth of populations and the impact of human activity on the environment.

Conclusion

P(t) = 350 * (1.05)^t

Introduction

In our previous article, we explored the concept of population growth in a bird enclosure at a zoo. We determined that the function that accurately describes the population of birds in the enclosure over time is given by:

P(t) = 350 * (1.05)^t

In this article, we will answer some frequently asked questions about population growth in a bird enclosure.

Q: What is the initial population of birds in the enclosure?

A: The initial population of birds in the enclosure is 350.

Q: What is the rate of growth of the population?

A: The rate of growth of the population is 5% per year.

Q: How can I calculate the population of birds in the enclosure for a given time period?

A: To calculate the population of birds in the enclosure for a given time period, you can use the formula:

P(t) = 350 * (1.05)^t

where t is the time in years.

Q: What is the population of birds in the enclosure after 1 year?

A: After 1 year, the population of birds in the enclosure is:

P(1) = 350 * (1.05)^1 = 367.5

Q: What is the population of birds in the enclosure after 2 years?

A: After 2 years, the population of birds in the enclosure is:

P(2) = 350 * (1.05)^2 = 386.225

Q: What is the population of birds in the enclosure after 3 years?

A: After 3 years, the population of birds in the enclosure is:

P(3) = 350 * (1.05)^3 = 405.59375

Q: How can I use the exponential growth model to describe population growth in other contexts?

A: The exponential growth model can be used to describe population growth in a variety of contexts, including:

Biology: The exponential growth model can be used to describe the growth of populations of animals, plants, and microorganisms.
Economics: The exponential growth model can be used to describe the growth of investments and the value of assets over time.
Finance: The exponential growth model can be used to describe the growth of populations and the impact of human activity on the environment.

Q: What are some real-world applications of the exponential growth model?

A: Some real-world applications of the exponential growth model include:

Population growth: The exponential growth model is often used to describe population growth in a variety of contexts, including biology, economics, and finance.
Epidemiology: The exponential growth model is used to describe the spread of diseases and the growth of populations.
Finance: The exponential growth model is used to describe the growth of investments and the value of assets over time.
Environmental science: The exponential growth model is used to describe the growth of populations and the impact of human activity on the environment.

Conclusion

In this article, we have answered some frequently asked questions about population growth in a bird enclosure. We have also discussed the key features of the exponential growth model and its real-world applications.