Question

World Internet Users The number of Internet users in the world reached 500 million in 2001 . By the end of 2003 , the number increased \(43.8 \%\). By the end of 2004 , the number increased \(13.6 \%\) from \(2003 .\) By the end of 2006 the number increased \(33.8 \%\) from 2004. (Source: Internet World Stats) (a) Find the number of users at the end of 2003 . (b) Find the number of users at the end of 2004 . (c) Find the number of users at the end of 2006 . (d) Find the percent increase in the number of users from 2001 to 2006 .

Short answer

(a) The number of users at the end of 2003 is 718 million.\n(b) The number of users at the end of 2004 is 816.048 million.\n(c) The number of users at the end of 2006 is 1092.72 million.\n(d) The percent increase in the number of users from 2001 to 2006 is 118.54%.

Step-by-step solution

Calculate the Number of Internet Users at the End of 2003

In 2001, there were 500 million users. At the end of 2003, the number of users had increased by \(43.8\%\) from 2001. To find the number of users in 2003, increase the 2001 number by \(43.8\%\). Calculate \(43.8\%\) of 500 million and add it to 500 million.

Calculate the Number of Internet Users at the End of 2004

At the end of 2004, the number of users had increased by \(13.6\%\) from 2003. To find the number of users in 2004, increase the 2003 number by \(13.6\%\). Calculate \(13.6\%\) of the number of users found in step 1 and add it to the number of users in 2003.

Calculate the Number of Internet Users at the End of 2006

At the end of 2006, the number of users had increased by \(33.8\%\) from 2004. To find the number of users in 2006, increase the 2004 number by \(33.8\%\). Calculate \(33.8\%\) of the number of users found in step 2 and add it to the number of users in 2004.

Determine the Percentage Increase from 2001 to 2006

To find the total percentage increase in users from 2001 to 2006, divide the increase in number of users from 2001 to the number found in step 3 by the original 2001 number. Multiply the result by 100 to get the percentage increase.

Key concepts

Internet Users

Internet users have grown dramatically over the years. Understanding this growth can help us grasp how technology becomes an integral part of everyday life. In 2001, there were already 500 million people using the internet globally. Imagine how large this number seems and remember, that was just the beginning of the digital age.

Every few years, more people gain access to the internet. From 2001 to 2006, the growth of internet users was phenomenal. These years involved three significant increases, showing how quickly internet access spread:

• In 2003, there was a 43.8% increase from 2001 figures.
• In 2004, the growth continued with an additional 13.6% increase from the 2003 numbers.
• By 2006, the number of users had gone up by 33.8% from 2004.

Understanding these changes provides insight into how quickly technology adoption can escalate. This context can be vital for anyone studying internet history, technology's role in society, or digital trends.

Percentage Calculation

Percentage calculations are often used when observing changes over time, like our internet user example. A percentage describes a part per hundred of a whole. To calculate how much something has increased, you can use a simple multiplier.

Let's review how to calculate percentage increases with an example:

• First, determine the percentage increase. For instance, a 43.8% increase means every whole (like 500 million users) increases by 43.8 out of 100 parts.
• Convert the percentage into a decimal for easier calculation. For 43.8%, you would use 0.438.
• Multiply the original number (500 million) by this decimal: \[ 500 \text{ million} \times 0.438 = 219 \text{ million} \]
• Add this result to the original to find the total new amount:\[ 500 \text{ million} + 219 \text{ million} = 719 \text{ million} \]

Percentage calculation turns data into something more meaningful by highlighting growth or declines.

Growth Rate Calculation

Growth rate calculation helps us understand the pace at which something increases over time. This concept is vital for areas like economics, population studies, and technology, much like with our example of internet users. It essentially measures how fast an initial amount grows to a final quantity.

Here's a step-by-step on how you can calculate growth rates:

• Find the starting and ending amounts. For our internet users example, you start with the number of users in 2001 and end with the number in 2006.
• Subtract the initial value from the final value to find the increase. This is your actual growth.
• Divide the growth amount by the initial number to find the growth rate.\[ \frac{\text{New amount - original amount}}{\text{original amount}} \]
• Multiply by 100 to convert to a percentage. This gives you the growth rate as a percentage.\[ \left(\frac{\text{New amount - original amount}}{\text{original amount}}\right) \times 100 \]

Calculating growth rates provides a clear picture of trends. It turns raw numbers into understandable insights on how quickly something is growing or declining.