Problem 32 - Intermediate Algebra

Question

Greenhouse Gases. The U.S. energy-related carbon dioxide emissions in 2008 were \(5,802\) million metric tons. In 2007 , that figure was \(5,967\) million metric tons. Find the percent of decrease and round to the nearest tenth of one percent. (Source: Energy Information Administration)

Step-by-Step Solution

Answer

The percent decrease in emissions was approximately 2.8%.

Step 1: Determine the Decrease in Emissions

First, find the difference in carbon dioxide emissions between the years 2007 and 2008. Subtract the emissions in 2008 from the emissions in 2007: \[ 5,967 - 5,802 = 165 \]This means there was a decrease of 165 million metric tons.

Step 2: Calculate the Percent Decrease

To find the percent decrease, divide the decrease in emissions by the original amount (the amount in 2007) and multiply by 100% to convert it to a percentage:\[ \text{Percent Decrease} = \left( \frac{165}{5,967} \right) \times 100 \%\approx 2.764 \% \]

Step 3: Round the Percent Decrease to the Nearest Tenth

The percent decrease calculated is approximately 2.764%. To round to the nearest tenth, look at the hundredths digit, which is 6. Since it is 5 or more, round up the tenths digit:\[ \text{Rounded Percent Decrease} = 2.8\% \]

Key Concepts

Calculating a Step-by-Step Solution

Understanding how to calculate the percent decrease using a step-by-step approach is essential for solving many real-world problems. Let's break this process down:

• Step 1: Determine the Decrease – First, find the difference between the two given values. In the exercise, we subtract the carbon dioxide emissions in 2008 from those in 2007 to find a decrease of 165 million metric tons. This gives us the basis for our calculations. Without this, you can't proceed to calculate the percent change.
• Step 2: Calculate the Percent Decrease – To find how much percent the value has decreased, divide the decrease by the original amount. We then multiply by 100% to convert this into a percentage. This is shown as \( \left( \frac{165}{5,967} \right) \times 100 \% \approx 2.764 \% \).
• Step 3: Rounding – The last step is rounding our calculated percentage to make it more understandable. Here we have 2.764%, which, rounded to the nearest tenth, becomes 2.8%.

These steps form the backbone of calculating percent decreases and are applicable to various types of data, ensuring a clear and accurate solution every time.

Understanding Carbon Dioxide Emissions

Carbon dioxide (CO2) emissions are a major contributor to global warming and climate change. They arise primarily from the burning of fossil fuels such as coal, oil, and natural gas.

In the U.S. example from the exercise, we see emissions data from 2007 and 2008. CO2 levels fluctuating from year to year can have significant implications for environmental policies and help inform strategies for reducing emissions.

By assessing a decrease of 165 million metric tons of CO2, we can view efforts toward cleaner energy as having a tangible impact. Understanding how to calculate such decreases contributes to making informed decisions and taking action where necessary. Every slight reduction holds importance when considering long-term environmental health.

The Importance of Rounding Percentages

Rounding percentages is an important skill for simplifying data and making it easier for others to understand quickly. When rounding, you decide based on the digit following the desired decimal place.

In our example, we calculated a 2.764% decrease in emissions. Let’s see how we round this to the nearest tenth:

• Identify the Tenths – We start with the first decimal place, which is 7 in 2.764.
• Check the Hundredths – Look at the next digit, which is 6. If this digit is 5 or more, you increase the tenths by one.
• Round Up – Since the hundredths digit is 6 (greater than 5), we round 2.764 up to become 2.8%.

Rounding serves to present a cleaner figure in reports and discussions and avoids overwhelming others with overly precise numbers. This practice renders data more accessible and actionable, supporting clearer communication among a wider audience.