Threatened monarch butterflies are monitored by measuring the area occupied by overwintering butterflies in Mexico. According to data collected by World Wildlife Fund Mexico, monarch butterflies occupied 0.67 hectares one recent winter, and 1.13 hectares the following winter (one year later)1. If the population is growing geometrically and grows at the same rate, how much area should the overwintering butterflies occupy one year after that

step 1: nitrogen fixation- conversion of atmospheric no₂ into forms useful to plants by lightning, bacteria, and cyanobacteria.

step 2: nitrification-process of converting ammonia to nitrite or nitrate.

step 3: assimilation-plant roots absorb new form of nitrogen.

step 4: ammonification-conversion of organic nitrogen to ammonia by bacteria involved in decomposition.

step 5: denitrification-bacteria turns the decomposed matter back into n₂o, which is released into atmosphere; repeat cycle.