A biologist tracks the number of bacteria living in a water tank. The biologist used a function that represents the amount of a certain chemical solution that is added to the water.

When the water has no chemicals, the number of bacteria (b) is 1200 per gallon.

For each tablespoon of the chemical solution (c) added to each gallon of water, the number of bacteria decreases by 75 per gallon.

How much of the chemical, in tablespoons, must be added to a 500-gallon tank to reduce the bacteria count to a safe 300 bacteria per gallon?

Question

Mathematics

Kamryn

25 November, 01:00

A biologist tracks the number of bacteria living in a water tank. The biologist used a function that represents the amount of a certain chemical solution that is added to the water.

When the water has no chemicals, the number of bacteria (b) is 1200 per gallon.

For each tablespoon of the chemical solution (c) added to each gallon of water, the number of bacteria decreases by 75 per gallon.

How much of the chemical, in tablespoons, must be added to a 500-gallon tank to reduce the bacteria count to a safe 300 bacteria per gallon?

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Answers (1)

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Kiersten · Answer 1

The equation that would best represent this biological scenario is,

N = 1200x - 75cx

where N is the number of bacteria, x is the number of gallon and c is the amount of chemical solution in tablespoon.

Calculating for the number of bacteria in situation 2.

300 (500) = (1200) (500) - (75) (500) (c)

The value of c from the equation is 12 tablespoons.