Problem 2
Question
Birth and death rates are often reported as births or deaths per thousand members of the population. What is the relative rate of growth of a population with a birth rate of 30 births per 1000 and a death rate of 20 deaths per 1000 ?
Step-by-Step Solution
Verified Answer
The relative growth rate is 10 per 1000 people.
1Step 1: Understand Relative Growth Rate
The relative rate of growth of a population is calculated as the difference between the birth rate and the death rate. This describes how much the population is expected to grow or shrink based on these two factors alone.
2Step 2: Identify the Given Rates
You are given a birth rate (\(b\)) of 30 births per 1000 people and a death rate (\(d\)) of 20 deaths per 1000 people.
3Step 3: Calculate the Relative Growth Rate
Subtract the death rate from the birth rate to find the relative growth rate: \[\text{Relative Growth Rate} = b - d = 30 - 20.\]
4Step 4: Simplify and Interpret
Calculate \(30 - 20\) which equals \(10\). This means the relative growth rate is 10 per 1000 people, indicating the population grows by 10 individuals per 1000 people per year.
Key Concepts
Understanding Birth RateExploring Death RateRelative Growth Rate Explained
Understanding Birth Rate
The birth rate is a way to measure how a population changes over time, specifically by looking at the number of newborns. It is generally calculated as the number of births per 1000 individuals in a given population per year. The birth rate provides insight into how quickly a population might increase, and it is a pivotal factor in understanding population dynamics.
In many countries, policies and social factors can impact birth rates. Access to healthcare, family planning services, economic stability, and cultural norms all play roles in determining whether a population's birth rate is likely to rise or fall. Meanwhile, higher birth rates often indicate a younger population, whereas lower birth rates might suggest an aging population.
Key points to remember:
In many countries, policies and social factors can impact birth rates. Access to healthcare, family planning services, economic stability, and cultural norms all play roles in determining whether a population's birth rate is likely to rise or fall. Meanwhile, higher birth rates often indicate a younger population, whereas lower birth rates might suggest an aging population.
Key points to remember:
- The birth rate provides data on the number of new births per 1000 people annually.
- Factors affecting birth rate include healthcare, economy, and cultural practices.
- Birth rates help to forecast demographic changes in a society.
Exploring Death Rate
The death rate is another crucial metric in population dynamics and represents the number of deaths per 1000 members of a population per year. Understanding the death rate helps demographers, government officials, and researchers to plan for healthcare, housing, and other resource needs in a society.
The death rate can be influenced by various factors like health care quality, disease prevalence, natural disasters, and overall living conditions. A high death rate might point to issues such as inadequate healthcare or environmental challenges. Conversely, a low death rate can suggest good healthcare services and a healthy environment.
Some essential points about the death rate include:
The death rate can be influenced by various factors like health care quality, disease prevalence, natural disasters, and overall living conditions. A high death rate might point to issues such as inadequate healthcare or environmental challenges. Conversely, a low death rate can suggest good healthcare services and a healthy environment.
Some essential points about the death rate include:
- It identifies the number of deaths per 1000 individuals annually.
- It's influenced by healthcare, environmental conditions, and social circumstances.
- It aids in predicting healthcare needs and other policy decisions.
Relative Growth Rate Explained
The relative growth rate indicates how quickly a population is increasing or decreasing, based solely on the given birth and death rates. It is calculated by subtracting the death rate from the birth rate. If the birth rate exceeds the death rate, the population is growing. Otherwise, it might be shrinking.
For instance, given a birth rate of 30 and a death rate of 20 per 1000 individuals, the relative growth rate would be calculated as follows: - Subtract the death rate from the birth rate: \[\text{Relative Growth Rate} = 30 - 20 = 10\text{ per 1000 people}\].This means for every 1000 individuals, the population would grow by 10 people annually.
Important aspects of relative growth rate:
For instance, given a birth rate of 30 and a death rate of 20 per 1000 individuals, the relative growth rate would be calculated as follows: - Subtract the death rate from the birth rate: \[\text{Relative Growth Rate} = 30 - 20 = 10\text{ per 1000 people}\].This means for every 1000 individuals, the population would grow by 10 people annually.
Important aspects of relative growth rate:
- It shows whether a population is growing or declining.
- Calculated by subtracting death rate from birth rate.
- A positive result means growth; a negative one suggests decline.
Other exercises in this chapter
Problem 1
A town has a population of 1000 . Fill in the table assuming that the town's population grows by (a) 50 people per year (b) \(5 \%\) per year $$ \begin{array}{c
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Draw a graph, with time in years on the horizontal axis, of what an income stream might look like for a company that sells sunscreen in the northeast United Sta
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Find the average value of \(g(t)=1+t\) over the interval \([0,2]\)
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(a) Find the present and future value of an income stream of \(\$ 6000\) per year for a period of 10 years if the interest rate, compounded continuously, is \(5
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