Solve the Problem A Use Regression to Find a Quadratic Function to Model

question 75

Essay

Solve the problem.
-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. $\begin{array}{l|llllllllllll}t & 8 & 16 & 24 & 32 & 40 & 48 & 56 & 64 & 72 & 80 & 88 & 96 \\\hline y(t) & 0.55 & 1.13 & 1.62 & 1.80 & 1.88 & 1.98 & 1.92 & 1.78 & 1.51 & 1.33 & 0.69 & 0.13\end{array}$

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.
A) a. $y = - 0.000831 t ^ { 2 } + 0.081 t + 0.028$
b. $51 \mathrm { hr }$

B) a. $y = - 0.0008148 t ^ { 2 } + 0.08155 t + 0.646$
b. $49 \mathrm { hr }$

C) a. $y = - 0.0008148 t ^ { 2 } + 0.08155 t + 0.646$
b. $50 \mathrm { hr }$

D) a. $y = - 0.000831 t ^ { 2 } + 0.081 t + 0.028$
b. $49 \mathrm { hr }$

• A) a. \(y = - 0.000831 t ^ { 2 } + 0.081 t + 0.028\)
• b. \(51 \mathrm { hr }\)
• B) a. \(y = - 0.0008148 t ^ { 2 } + 0.08155 t + 0.646\)
• b. \(49 \mathrm { hr }\)
• C) a. \(y = - 0.0008148 t ^ { 2 } + 0.08155 t + 0.646\)
• b. \(50 \mathrm { hr }\)
• D) a. \(y = - 0.000831 t ^ { 2 } + 0.081 t + 0.028\)
• b. \(49 \mathrm { hr }\)

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