Final answer:
The amount of CO2 in the atmosphere increases option (c) each year due to the exponential growth factor in the model A decade(t), and every year it increases by the 10th root of 1.06, which is a multiplication factor, not an additive one.
Step-by-step explanation:
The amount of carbon dioxide (CO2) in the atmosphere is modeled by the function A decade(t) = 315 * (1.06)t, where t is the elapsed time in decades since CO2 levels were first measured, and the total amount of CO2 is in parts per million.
To determine the yearly rate of change, we need to consider how the function changes with each year, which is a fraction of a decade. If we interpret 'factor' as the rate of change per year based on the exponential model, the amount of CO2 increases by a factor of the 10th root of 1.06 each year, because (1.06)1/10 represents the annual increase factor within a decade. However, this factor is a multiplication factor, not an additive one.
Every year, the amount of CO2 does not remain constant; nor does it decrease. Instead, it increases each year due to the exponential growth factor present in the function. Hence, there is a compounding effect, not a simple multiplication by 1.06 each year.
Therefore, Option C is the closest to the true yearly increase, although it's not a direct multiplication by 1.06 each year by the 10th root of 1.06 due to the way the function is structured over decades.