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Tetanus bacillus bacteria are cultured to produce tetanus toxin used in an inactive form for the tetanus vaccine. The amount of toxin produced per batch increases with time and then decreases as the culture becomes unstable. The variable t is the time in hours after the culture has started, and y(t) is the yield of toxin in grams. 8 16 24 32 40 48 y(t) 0.60 1.12 1.60 1.78 1.90 2.00 56 64 72 80 88 96 y(t) 1.94 1.80 1.48 1.30 0.66 0.10 a. Use regression to find a quadratic function to model the data. b. At what time is the yield the greatest? Round to the nearest hour. c. What is the maximum yield? Round to the nearest gram.

Tetanus bacillus bacteria are cultured to produce tetanus toxin used in an inactive form for the tetanus vaccine. The amount of toxin produced per batch increases with time and then decreases as the culture becomes unstable. The variable t is the time in hours after the culture has started, and y(t) is the yield of toxin in grams. 8 16 24 32 40 48 y(t) 0.60 1.12 1.60 1.78 1.90 2.00 56 64 72 80 88 96 y(t) 1.94 1.80 1.48 1.30 0.66 0.10 a. Use regression to find a quadratic function to model the data. b. At what time is the yield the greatest? Round to the nearest hour. c. What is the maximum yield? Round to the nearest gram.

Functions and Change: A Modeling Approach to College Algebra (MindTap Course List)
Functions and Change: A Modeling Approach to College Algebra (MindTap Course List)
6th Edition
ISBN:9781337111348
Author:Bruce Crauder, Benny Evans, Alan Noell
Publisher:Bruce Crauder, Benny Evans, Alan Noell
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Tetanus bacillus bacteria are cultured to produce tetanus toxin used in an inactive form for the tetanus vaccine. The amount of toxin produced per batch increases with time and then decreases as the culture becomes unstable. The variable t is the time in hours after the culture has started, and y(t) is the yield of toxin in grams. 8 16 24 32 40 48 y(t) 0.60 1.12 1.60 1.78 1.90 2.00 56 64 72 80 88 96 y(t) 1.94 1.80 1.48 1.30 0.66 0.10 a. Use regression to find a quadratic function to model the data. b. At what time is the yield the greatest? Round to the nearest hour. c. What is the maximum yield? Round to the nearest gram.
Transcribed Image Text:Tetanus bacillus bacteria are cultured to produce tetanus toxin used in an inactive form for the tetanus vaccine. The amount of toxin produced per batch increases with time and then decreases as the culture becomes unstable. The variable t is the time in hours after the culture has started, and y(t) is the yield of toxin in grams. 8 16 24 32 40 48 y(t) 0.60 1.12 1.60 1.78 1.90 2.00 56 64 72 80 88 96 y(t) 1.94 1.80 1.48 1.30 0.66 0.10 a. Use regression to find a quadratic function to model the data. b. At what time is the yield the greatest? Round to the nearest hour. c. What is the maximum yield? Round to the nearest gram.
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