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) Activity, r (U/100μL) 0.10 0.10 4 0.25 0.60 1.00 1.40 10 1.55 12 14 1.75 16 1.90 1.95 18 (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 0sts 18. (Round all numerical values to three decimal places.) r(t) = U/100µL 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 3 minutes and 11 minutes. (Round your answer to three decimal places.) U/100UL per minute (c) Numerically estimate to the nearest thousandth by how much the reaction activity is increasing at 5 minutes. (Round your answer to three decimal places.) U/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 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) Activity, r (U/100μL) 0.10 0.10 4 0.25 0.60 1.00 1.40 10 1.55 12 14 1.75 16 1.90 1.95 18 (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 0sts 18. (Round all numerical values to three decimal places.) r(t) = U/100µL 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 3 minutes and 11 minutes. (Round your answer to three decimal places.) U/100UL per minute (c) Numerically estimate to the nearest thousandth by how much the reaction activity is increasing at 5 minutes. (Round your answer to three decimal places.) U/100µL per minute

College Algebra

1st Edition

ISBN:9781938168383

Author:Jay Abramson

Publisher:Jay Abramson

Chapter6: Exponential And Logarithmic Functions

Section6.7: Exponential And Logarithmic Models

Problem 4SE: Define Newton’s Law of Cooling. Then name at least three real-world situations where Newton’s Law of...

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