A chemical reaction begins when a certain mixture of chemicals reaches 95°C. The reaction activity is measured in units (U) per 100 microliters (100 μL) of the mixture. Measurements during the first 18 minutes after the mixture reaches 95°C are listed in the following table. Chemical Reaction Time, t (minutes) 0 2 4 r(t) = 6 8 10 12 14 16 18 Activity, r (U/100μL) 0.10 0.10 0.25 0.60 1.00 1.40 1.55 1.75 1.90 1.95 (a) Find the logistic model that gives the activity of the chemical reaction. (Be sure to use t as the independent variable. Round all numerical values to three decimal places.) 1.937 (1+29.0638e(-0.4211)) x U/100μL gives a measurement of the reaction activity of a chemical mixture -?- minutes after the mixture reaches a temperature of What is the limiting value for this logistic function? U/100μL (b) Use the model to estimate the average rate of change of the reaction activity between 9 minutes and 13 minutes. (Round your answer to three decimal places.) U/100μL per minute (c) Numerically estimate to the nearest thousandth by how much the reaction activity is increasing at 11 minutes. (Round your answer to three decimal places.) U/100μL per minute (d) Write sentences of interpretation for the answers to parts (b) and (c). (Round your answers to three decimal places.) Between 9 and 13 minutes after the mixture reached a temperature of 95°C, the reaction activity ---Select-- by an average of C. from Osts 18. U/100μL per minute. After 11 minutes, the reaction activity was ---Select---by U/100μL per minu
A chemical reaction begins when a certain mixture of chemicals reaches 95°C. The reaction activity is measured in units (U) per 100 microliters (100 μL) of the mixture. Measurements during the first 18 minutes after the mixture reaches 95°C are listed in the following table. Chemical Reaction Time, t (minutes) 0 2 4 r(t) = 6 8 10 12 14 16 18 Activity, r (U/100μL) 0.10 0.10 0.25 0.60 1.00 1.40 1.55 1.75 1.90 1.95 (a) Find the logistic model that gives the activity of the chemical reaction. (Be sure to use t as the independent variable. Round all numerical values to three decimal places.) 1.937 (1+29.0638e(-0.4211)) x U/100μL gives a measurement of the reaction activity of a chemical mixture -?- minutes after the mixture reaches a temperature of What is the limiting value for this logistic function? U/100μL (b) Use the model to estimate the average rate of change of the reaction activity between 9 minutes and 13 minutes. (Round your answer to three decimal places.) U/100μL per minute (c) Numerically estimate to the nearest thousandth by how much the reaction activity is increasing at 11 minutes. (Round your answer to three decimal places.) U/100μL per minute (d) Write sentences of interpretation for the answers to parts (b) and (c). (Round your answers to three decimal places.) Between 9 and 13 minutes after the mixture reached a temperature of 95°C, the reaction activity ---Select-- by an average of C. from Osts 18. U/100μL per minute. After 11 minutes, the reaction activity was ---Select---by U/100μL per minu
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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Transcribed Image Text:A chemical reaction begins when a certain mixture of chemicals reaches 95°C. The reaction activity is measured in units (U) per 100 microliters (100 μL) of the mixture. Measurements during the first 18 minutes after the mixture reaches 95°C are listed in the following table.
Chemical Reaction
Time, t
(minutes)
0
2
r(t) =
4
6
8
10
12
14
16
18
Activity, r
(U/100μL)
0.10
0.10
0.25
0.60
1.00
1.40
1.55
1.75
1.90
1.95
(a) Find the logistic model that gives the activity of the chemical reaction. (Be sure to use t as the independent variable. Round all numerical values to three decimal places.)
1.937
(1+29.0638e(-0.421r))
X
U/100μL gives a measurement of the reaction activity of a chemical mixture --?--✓ minutes after the mixture reaches a temperature of
What is the limiting value for this logistic function?
U/100μL
(b) Use the model to estimate the average rate of change of the reaction activity between 9 minutes and 13 minutes. (Round your answer to three decimal places.)
U/100μL per minute
(c) Numerically estimate to the nearest thousandth by how much the reaction activity is increasing at 11 minutes. (Round your answer to three decimal places.)
U/100μL per minute
(d) Write sentences of interpretation for the answers to parts (b) and (c). (Round your answers to three decimal places.)
Between 9 and 13 minutes after the mixture reached a temperature of 95°C, the reaction activity --Select---by an average of
°C, from 0 ≤ts 18.
U/100μL per minute. After 11 minutes, the reaction activity was --Select--- ✓ by
U/100μL per minute.
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