5. Find the rate of change of carbon in gigatons per year by subtracting the total amount removed (answer to Question 4) from the amount added (answer to Question 3) Answer:215-211.9-3.1 gigatons 7. Write the rate of change of atmospheric carbon (answer to Question 5), as a differential equation of the form dC/dt = some number. Where "some number" is the amount by which the amount of atmospheric carbon changes in the units of gigatons per year. Answer: 8. Integrate the differential equation in Question 7 above. The integral will be of the form: Jac = [(some (some number) dt Where "some number" is the same number from Question 7. After integrating the above expression, you will get an equation relating the amount of carbon on the left-hand side to how much it changes with time on the right-hand side. Show your steps of integration, and the resulting equation below. Answer: 9. Next, we will find the constant of integration (A). We will assume that the total atmospheric carbon is 730 gigatons in the year 2000 (the value listed next to "Atmosphere" in Figure 2 above. Substitute this value for the left-hand side in the equation you got in Question 8 and use time (t) = 2000. This will allow you to find the constant of integration (A). Show your calculations and answer below. Answer: