## Question

###### A chemical reaction begins when a certain mixture ofchemicals reaches 95Â°C. The reaction activity is measured in units(U) per 100 microliters (100 ÂµL) of the mixture. Measurementsduring the first 18 minutes after the mixture reaches 95Â°C arelisted in the following table.Chemical ReactionTime, t(minutes)Activity, r(U/100ÂµL)00.1020.1040.2560.6081.00101.40121.55141.75161.90181.95(a) Find the function for the logistic model that givesthe activity of the chemical reaction in U/100ðœ‡L, where t i

A chemical reaction begins when a certain mixture of chemicals reaches 95Â°C. The reaction activity is measured in units (U) per 100 microliters (100 ÂµL) of the mixture. Measurements during the first 18 minutes after the mixture reaches 95Â°C are listed in the following table. Chemical Reaction Time, t (minutes) Activity, r (U/100ÂµL) 0 0.10 2 0.10 4 0.25 6 0.60 8 1.00 10 1.40 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/100ðœ‡L, where t is the time in minutes after the mixture reaches a temperature of 95Â°C, with data from 0 â‰¤ t â‰¤ 18. (Round all numerical values to three decimal places.) r(t) = 1.936 (1+29.06eâˆ’0.42t) U/100ÂµL What is the limiting value for this logistic function? U/100ÂµL (b) Use the model to estimate the average rate of change of the reaction activity between 3 minutes and 7 minutes. (Round your answer to three decimal places.) U/100ÂµL 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/100ÂµL per minute (d) Write sentences of interpretation for the answers to parts (b) and (c). (Round your answers to three decimal places.) Between 3 and 7 minutes after the mixture reached a temperature of 95Â°C, the reaction activity ---Select--- increased decreased by an average of U/100ÂµL per minute. After 5 minutes, the reaction activity was ---Select--- increasing decreasing by U/100ÂµL per minute.