Problem 57 - College Algebra Essentials

Question

Writing in Mathematics Nigeria has a growth rate of 0.025 or \(2.5 \% .\) Describe what this means.

Step-by-Step Solution

Answer

A growth rate of 2.5% in Nigeria means that for every 100 units of a certain quantity (like population or economy), there is an expected increase of 2.5 units in a specific time period.

Step 1: Understanding Growth Rate

A growth rate of 2.5% means that, for every 100 units of a certain quantity (it could be population, economy, etc., the context is not specified in the problem), it is expected to increase by 2.5 units in a given time period (usually yearly).

Step 2: Applying it to Nigeria

Hence, in the context of Nigeria, if this is a population growth rate, it would mean that for every 100 people currently, we would expect an increase of 2.5 people per year. If it were an economic growth rate, it would mean that for every 100 units of currency in the economy, we would expect an increase of 2.5 units of currency per year, and so forth.

Key Concepts

Understanding Percentage Increase

When you hear about a percentage increase, it's all about understanding growth in terms of percentages. This concept is quite common in different fields, especially in areas dealing with growth and change. A 2.5% increase means that for every 100 units of whatever you're measuring, there is an additional 2.5 units after the increase. Let's look at what this means in simpler terms.

• If you start with something like 100 apples and they grow by 2.5%, you end up with 102.5 apples. You don't actually have half an apple, but mathematically speaking, it's how much the number of apples has theoretically increased.
• A percentage increase allows you to see growth proportionate to what you initially had. This is crucial because a bigger original amount will see a bigger numerical increase even if the percentage growth rate stays the same.

Whenever you are trying to understand growth in a mathematical or real-world scenario, remembering the concept of percentage increase is a helpful starting point.

Exploring Population Growth

Population growth is the increase in the number of individuals in a population. It's typically measured as a percentage, signifying how much the number of people grows over a specific period of time, usually a year. Having a growth rate of 2.5% would mean that for every 100 people living in a country like Nigeria, approximately 2.5 more people are added to the population each year.

• This growth can occur through natural means like birth rates exceeding death rates, or via migration where more people move into a region than those leaving it.
• Countries track population growth closely, as it has significant implications for economic development, resource needs, and urban planning.

Population growth helps governments and organizations plan for the future, ensuring that infrastructure, services, and resources can meet the demands of a growing population.

Analyzing Economic Growth

Economic growth refers to the increase in the production of economic goods and services within a country over a certain period, commonly measured annually. A growth rate of 2.5% for a country's economy implies that the total value of goods and services produced, known as Gross Domestic Product (GDP), will grow by 2.5% over one year.

• Economic growth is crucial as it often leads to a higher standard of living, more jobs, and improved public services.
• It can arise from various factors such as increased productivity, new technological advancements, and better education systems.

Governments and economists strive to achieve consistent economic growth as it typically leads to better opportunities and overall improvements in a country's prosperity.