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. t 8 16 24 32 40 48 56 64 72 80 88 96 y(t) 0.55 1.13 1.62 1.80 1.88 1.98 1.92 1.78 1.51 1.33 0.69 0.13 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.
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. t 8 16 24 32 40 48 56 64 72 80 88 96 y(t) 0.55 1.13 1.62 1.80 1.88 1.98 1.92 1.78 1.51 1.33 0.69 0.13 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.
Algebra and Trigonometry (6th Edition)
6th Edition
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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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.
| t | 8 | 16 | 24 | 32 | 40 | 48 | 56 | 64 | 72 | 80 | 88 | 96 |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| y(t) | 0.55 | 1.13 | 1.62 | 1.80 | 1.88 | 1.98 | 1.92 | 1.78 | 1.51 | 1.33 | 0.69 | 0.13 |
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.
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