The Bayside Community Water District has decided to add fluoride to the drinking water. Board member Evelyn King does research and finds that the ideal concentration of fluoride in drinking water is between 1.00 mg/L and 2.00 mg/L. If the concentration gets higher than 4.00 mg/L, people may suffer health problems, such as bone disease or damage to developing teeth. If the concentration is less than 1.00 mg/L, it is too low to promote dental health. Ms. King supposes 15% of the fluoride present in the water supply is consumed during a period of one day. Create a graph to help her analyze each of these scenarios. A water treatment plant
a. If the fluoride content begins at 3.00 mg/L and no additional fluoride is added, how long will it be before the concentration is too low to promote dental health?
b. If the fluoride content begins at 3.00 mg/L and 0.50 mg/L is added daily, will the concentration increase or decrease? What is the long-run value? Explain your reasoning.
c. Suppose the fluoride content begins at 3.00 mg/L and 0.10 mg/L is added daily.
Describe what happens.
d. The Water District board members vote that there should be an initial treatment of 3.00 mg/L, but that the long-run fluoride content should be 1.50 mg/L. How much fluoride needs to be added daily for the fluoride content to stabilize at 1.50 mg/L?