The temperature of Earth's surface is strongly influenced by the amount of carbon in the atmosphere. Each year, human activity adds another 9 gigatons of carbon to the atmosphere. 2 gigatons of this carbon is absorbed by the oceans, and 3 gigatons of this carbon is absorbed by plant growth (photosynthesis). There is currently 900 gigatons of carbon in the atmosphere. Let us make our a bit more model realistic. Instead of assuming a constant rate of absorption by plant growth, assume that the rate of carbon absorption by plant growth is proportional to the amount of carbon in the atmosphere at any time t. This increase constitutes 0.4% for each gigaton of carbon. Write down a differential equation for the total amount of carbon in the atmosphere over time. Solve the equation and use the solution to predict the equilibrium amount of carbon in the atmosphere.
The temperature of Earth's surface is strongly influenced by the amount of carbon in the atmosphere. Each year, human activity adds another 9 gigatons of carbon to the atmosphere. 2 gigatons of this carbon is absorbed by the oceans, and 3 gigatons of this carbon is absorbed by plant growth (photosynthesis). There is currently 900 gigatons of carbon in the atmosphere.
Let us make our a bit more model realistic. Instead of assuming a constant rate of absorption by plant growth, assume that the rate of carbon absorption by plant growth is proportional to the amount of carbon in the atmosphere at any time t. This increase constitutes 0.4% for each gigaton of carbon. Write down a differential equation for the total amount of carbon in the atmosphere over time. Solve the equation and use the solution to predict the equilibrium amount of carbon in the atmosphere.
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