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 decrease 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. (See Example 6) 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 decrease 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. (See Example 6) 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.
Solution Summary: The author analyzes the quadratic function of the following data by using Ti-83 graphing calculator.
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 decrease 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. (See Example 6)
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.
2. Suppose the population of Wakanda t years after 2000 is given by the equation
f(t) = 45000(1.006). If this trend continues, in what year will the population reach 50,000
people? Show all your work, round your answer to two decimal places, and include units. (4
points)
3. Solve the equation, give the answer exactly (no calculator approximations), and show all your
work. (4 points)
log5 2x = 3
Let I =
f(x) dx, where f is the function whose graph is shown.
4
2
y
f
X
1
2
3
4
(a) Use the graph to find L2, R2 and M2.
R₂
M2
=
=
=
(b) Are these underestimates or overestimates of I?
O 42 is an underestimate.
O 42 is an overestimate.
◇ R2 is an underestimate.
OR2 is an overestimate.
OM2 is an underestimate.
○ M2 is an overestimate.
(c) Use the graph to find T2.
T₂ =
University Calculus: Early Transcendentals (4th Edition)
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