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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 HL) 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) Activity, r (υ/ 100μL) 0 0.10 2 0.10 0.25 6 0.60 1.00 8 1.40 10 12 1.55 14 1.75 16 1.90 18 1.95 (a) Find the function for the logistic model that gives the activity of the chemical reaction in U/100UL, where t is the time in minutes after the mixture reaches a temperature of 95°C, with data from 0 Sts 18. (Round all numerical values to three decimal places.) υ/100μL r(t) 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 7 minutes and 15 minutes. (Round your answer to three decimal places.) U/100pL per minute (c) Numerically estimate to the nearest thousandth by how much the reaction activity is increasing at 9 minutes. (Round your answer to three decimal places.) U/100HL per minute (d) Write sentences of interpretation for the answers to parts (b) and (c). (Round your answers to three decimal places.) U/100uL per minute. After 9 minutes, the reaction activity wasSelect Between 7 and 15 minutes after the mixture reached a temperature of 95°C, the reaction activitySelect by an average of by υ/100μL per minute.

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 HL) 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) Activity, r (υ/ 100μL) 0 0.10 2 0.10 0.25 6 0.60 1.00 8 1.40 10 12 1.55 14 1.75 16 1.90 18 1.95 (a) Find the function for the logistic model that gives the activity of the chemical reaction in U/100UL, where t is the time in minutes after the mixture reaches a temperature of 95°C, with data from 0 Sts 18. (Round all numerical values to three decimal places.) υ/100μL r(t) 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 7 minutes and 15 minutes. (Round your answer to three decimal places.) U/100pL per minute (c) Numerically estimate to the nearest thousandth by how much the reaction activity is increasing at 9 minutes. (Round your answer to three decimal places.) U/100HL per minute (d) Write sentences of interpretation for the answers to parts (b) and (c). (Round your answers to three decimal places.) U/100uL per minute. After 9 minutes, the reaction activity wasSelect Between 7 and 15 minutes after the mixture reached a temperature of 95°C, the reaction activitySelect by an average of by υ/100μL per minute.

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter2: Equations And Inequalities
Section2.1: Equations
Problem 74E
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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 HL) 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) Activity, r (υ/ 100μL) 0 0.10 2 0.10 0.25 6 0.60 1.00 8 1.40 10 12 1.55 14 1.75 16 1.90 18 1.95 (a) Find the function for the logistic model that gives the activity of the chemical reaction in U/100UL, where t is the time in minutes after the mixture reaches a temperature of 95°C, with data from 0 Sts 18. (Round all numerical values to three decimal places.) υ/100μL r(t) 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 7 minutes and 15 minutes. (Round your answer to three decimal places.) U/100pL per minute (c) Numerically estimate to the nearest thousandth by how much the reaction activity is increasing at 9 minutes. (Round your answer to three decimal places.) U/100HL per minute (d) Write sentences of interpretation for the answers to parts (b) and (c). (Round your answers to three decimal places.) U/100uL per minute. After 9 minutes, the reaction activity wasSelect Between 7 and 15 minutes after the mixture reached a temperature of 95°C, the reaction activitySelect by an average of by υ/100μL per minute.
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 HL) 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) Activity, r (υ/ 100μL) 0 0.10 2 0.10 0.25 6 0.60 1.00 8 1.40 10 12 1.55 14 1.75 16 1.90 18 1.95 (a) Find the function for the logistic model that gives the activity of the chemical reaction in U/100UL, where t is the time in minutes after the mixture reaches a temperature of 95°C, with data from 0 Sts 18. (Round all numerical values to three decimal places.) υ/100μL r(t) 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 7 minutes and 15 minutes. (Round your answer to three decimal places.) U/100pL per minute (c) Numerically estimate to the nearest thousandth by how much the reaction activity is increasing at 9 minutes. (Round your answer to three decimal places.) U/100HL per minute (d) Write sentences of interpretation for the answers to parts (b) and (c). (Round your answers to three decimal places.) U/100uL per minute. After 9 minutes, the reaction activity wasSelect Between 7 and 15 minutes after the mixture reached a temperature of 95°C, the reaction activitySelect by an average of by υ/100μL per minute.
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