Question

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?

Answer 1

Answer: 6000

Explanation:

Number of bacteria in 500 gallon tank before treatment : 500×1200=600000

Number of bacteria allowed in 500 gallon tank : 500×300=150000

Number of bacteria need to be removed from 500 gallon tank : 600000-150000=450000

Number of tablespoons must be added to reduce the bacteria count to a safe 300 bacteria per gallon:

450000 ÷ 75 = 6000 tablespoons

Hope that helps you.

Answer 2

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.