A biologist measures the amount of contaminant in a lake 2 hours after a chemical spill and again 11 hours after the spill. She sets up two possible models to determine Q, the amount of the chemical remaining in the lake as a function of t, the time in hours since the spill. The first model assumes the contaminant is leaving the lake at a constant rate, which she determines to be 3 tons/hour. Using this model, she estimates that the lake will be free from the contaminant 25 hours after the spill. The second model assumes that the amount of contaminant decreases exponentially. She measures the spill a third time after 18 hours and finds that 29 tons remain. Which model seems best?
A) The linear one
B) The exponential one

Question

Quizplus · Accepted Answer

The exponential model is likely more accurate because the amount of contaminant does not decrease at a constant rate, as evidenced by the third measurement. In real scenarios, contaminants often degrade or are diluted in a manner that is better represented by an exponential decay, especially given the data point at 18 hours showing 29 tons remain, which does not align with a constant rate of removal.

A Biologist Measures the Amount of Contaminant in a Lake