) = 80e−0.05t + 8(t + 1)−0.5. Her model says that C(t) is the number of coliform group bacteria colonies at time t, where t is measured in minutes since the tablet was added to the water. (a) According to this model, how many coliform group bacteria colonies would initially be in a 2 L sample of the water?
the scientist is studying the effect of water purification tablets on the creek water in her local area. She collected several different 2 L samples from a creek. For each sample, she measured the number of coliform group bacteria colonies in the water initially, and then added a water purification tablet and measured the number of coliform group bacteria colonies over time. She found that the following equation was a good fit to the data:
C(t) = 80e−0.05t + 8(t + 1)−0.5.
Her model says that C(t) is the number of coliform group bacteria colonies at time t, where t is
measured in minutes since the tablet was added to the water.
(a) According to this model, how many coliform group bacteria colonies would initially be in a 2 L sample of the water?
background information:
The quality of drinking water is determined by tests for coliform group bacteria, which are organisms found in soil and in the intestinal tract of warm-blooded animals. Coliform group bacteria are not considered to be a pathogen, but their presence in water indicates pathogenic contamination. The standard for drinking water is less than 1 coliform colony per 100 millilitres of sample.
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