Carbon emissions from China and the United States The...

Carbon emissions from China and the United States The burning of fossil fuels releases greenhouse gases into the atmosphere. In $1995,$ the United States emitted about 1.4 billion tons of carbon into the atmosphere, nearly one-fourth of the world total. China was the second largest contributor, emitting about 850 million tons of carbon. However, emissions from China were rising at a rate of about $4 \% / \mathrm{yr}$, while U.S. emissions were rising at about $1.3 \% /$ yr. Using these growth rates, project greenhouse gas emissions from the United States and China in $2020 .$ Graph the projected emissions for both countries. Comment on your observations.

Key Concepts

Data Visualization

Data visualization is the process of graphically representing information to make patterns, trends, and correlations more accessible and understandable. In the context of projecting emissions, creating graphs can effectively compare growth trends between different sources or countries, thereby facilitating a clearer understanding of the data and its implications.

Greenhouse Gas Emissions

Greenhouse gas emissions refer to the release of gases, such as carbon dioxide, methane, and others, that trap heat in the Earth's atmosphere. This concept is central to discussions on global warming and climate change since increased emissions, primarily from the burning of fossil fuels, contribute significantly to rising global temperatures.

Fossil Fuels

Fossil fuels, including coal, oil, and natural gas, are energy sources that, when burned, release carbon dioxide and other pollutants into the atmosphere. Their combustion is the primary source of anthropogenic greenhouse gas emissions, making them critical to understanding environmental impact and policy decisions.

Exponential Growth and Compound Interest

Exponential growth describes a process where a quantity increases by a fixed percentage over consistent time intervals. Applying this concept through the compound growth formula allows for projection of future values, such as estimating greenhouse gas emissions over time based on current growth rates.

Emission Projections

Emission projections involve estimating future greenhouse gas outputs using current data and growth rates. This key concept helps policymakers and scientists understand potential future scenarios and the urgency of implementing strategies to mitigate climate change.

Transcript

00:01 We're given the number of tons of carbon emitted from the u .s.

00:04 And china, and then a growth rate per year for each country.

00:09 And we want to find how much carbon is emitted after 25 years for the u .s.

00:14 And for china.

00:15 And then we want to graph u of t and c of t for each country against each other to see what the differences are and what we can learn from that graph.

00:25 So we'll start by looking for the u .s.

00:28 We know it's 25 years because it started in 1995 and we want the year 2020.

00:37 That's how we got that 25.

00:39 We'll look at our equation.

00:41 U of t is equal to u0 our initial amount times e to the k t because this is exponential growth.

00:49 So we'll get 1 .4.

00:51 We know it's growing so we're going to do it in billions because the numbers will get bigger but not smaller.

00:56 So 1 .4 e to the k t we need this k value.

01:00 We know that in one year, u of 1 is equal to 1 .4e to the k times t is 1.

01:09 And we also know from a growth rate of 1 .3 % that there will be 101 .3 % the amount in one year.

01:17 So we can write that as 1 .03 times 1 .4.

01:22 And these will be equal to each other.

01:24 We can solve for our k value.

01:27 Our 1 .4 is we'll cancel.

01:29 We'll get e to the k is equal to 1 .013.

01:33 And that gives us that k is equal to the natural log of 1 .03.

01:40 And then we can plug this back into our equation.

01:42 U of t is equal to 1 .4 times e to the t times our k, natural log of 1 .013.

01:52 Now we have a t outside a natural log, so we can send that into the exponent.

01:56 And then we have e to a natural log in its exponent, and so those will cancel.

02:01 So we'll get, this is also equal to 1 .4 times 1 .013 to the t...

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