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2. A chemical reaction proceeds in such a way that after the first second, the amount of a certain chemical involved in the reaction changes at a rate thať's inversely proportional to the product of the mass of the chemical present (in grams) and the time elapsed since the reaction began (in seconds). A. The mass m = m(t) of this chemical is modeled with what differential equation for time t > 1 second? B. The solution to the differential equation modeling the mass m of the chemical at time t seconds is m(t) how this equation is derived from your answer in part A. 2k Int + C for t > 1, where k and C are undetermined constants. Show C. Suppose that the amount of this chemical involved in the reaction is 40 grams at time t = 1 second and 30 grams at time t = 10 seconds. Find an explicit equation for the mass m of the chemical as a function of t, for t 2 1. Your equation should not involve any unknown constants or any calculator numbers. D. According to your equation for m(t) in part C, at what time does the mass of the chemical involved in the reaction become zero? (You may use your calculator here.)

2. A chemical reaction proceeds in such a way that after the first second, the amount of a certain chemical involved in the reaction changes at a rate thať's inversely proportional to the product of the mass of the chemical present (in grams) and the time elapsed since the reaction began (in seconds). A. The mass m = m(t) of this chemical is modeled with what differential equation for time t > 1 second? B. The solution to the differential equation modeling the mass m of the chemical at time t seconds is m(t) how this equation is derived from your answer in part A. 2k Int + C for t > 1, where k and C are undetermined constants. Show C. Suppose that the amount of this chemical involved in the reaction is 40 grams at time t = 1 second and 30 grams at time t = 10 seconds. Find an explicit equation for the mass m of the chemical as a function of t, for t 2 1. Your equation should not involve any unknown constants or any calculator numbers. D. According to your equation for m(t) in part C, at what time does the mass of the chemical involved in the reaction become zero? (You may use your calculator here.)

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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2. A chemical reaction proceeds in such a way that after the first second, the amount of a certain chemical involved in the reaction changes at a rate thať's inversely proportional to the product of the mass of the chemical present (in grams) and the time elapsed since the reaction began (in seconds). A. The mass m = m(t) of this chemical is modeled with what differential equation for time t > 1 second? B. The solution to the differential equation modeling the mass m of the chemical at time t seconds is m(t) how this equation is derived from your answer in part A. 2k Int + C for t > 1, where k and C are undetermined constants. Show C. Suppose that the amount of this chemical involved in the reaction is 40 grams at time t = 1 second and 30 grams at time t = 10 seconds. Find an explicit equation for the mass m of the chemical as a function of t, for t 2 1. Your equation should not involve any unknown constants or any calculator numbers. D. According to your equation for m(t) in part C, at what time does the mass of the chemical involved in the reaction become zero? (You may use your calculator here.)
Transcribed Image Text:2. A chemical reaction proceeds in such a way that after the first second, the amount of a certain chemical involved in the reaction changes at a rate thať's inversely proportional to the product of the mass of the chemical present (in grams) and the time elapsed since the reaction began (in seconds). A. The mass m = m(t) of this chemical is modeled with what differential equation for time t > 1 second? B. The solution to the differential equation modeling the mass m of the chemical at time t seconds is m(t) how this equation is derived from your answer in part A. 2k Int + C for t > 1, where k and C are undetermined constants. Show C. Suppose that the amount of this chemical involved in the reaction is 40 grams at time t = 1 second and 30 grams at time t = 10 seconds. Find an explicit equation for the mass m of the chemical as a function of t, for t 2 1. Your equation should not involve any unknown constants or any calculator numbers. D. According to your equation for m(t) in part C, at what time does the mass of the chemical involved in the reaction become zero? (You may use your calculator here.)
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