Volcanic carbon dioxide δ13C is –5‰. The average δ13C of the climate system before the PETM was –1.45‰. The magnitude of change during the PETM was δ13C was –3‰. Use the following isotopic mass balance equation to calculate how much volcanic carbon would have to be added to the climate system at the start of the PETM in order to produce the isotopic change observed. MX is the mass of carbon at time X, (δ13C)X is the δ13C at time X.