a) A maintenance staff member of the company has found that water tank is affected bysome bacteria few days ago. Bacteria population grows at a rate proportional to thepopulation. There were 100 bacteria 4 days ago and 1200 bacteria 1 day ago when thewater samples were tested in a lab.i)ii)Form the differential equation according to the given scenario.Predict the expected number of bacteria by tomorrow.b) The R & D department of the company is testing whether radioactive materials can beused as fuels in future. The weight W of a certain radioactive material decays at a rateproportional to the weight. The half-life is 3000 seconds. The original weight is 35 grams.The scientists in the R & D department are interested in finding the weight of theradioactive material after t seconds.

Answered: Image /qna-images/answer/a3a1175c-3479-4358-bf1f-9a2b68e95de4.jpg

Answered: a) A maintenance staff member of the…

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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Determine whether -log (1- 9(1-) is a good cost function for logistic regression 1+e07 when y = 0. Explain.
An investigation was carried out to study the relationship between speed (ft/sec) and stride rate (number of steps taken/sec) among female marathon runners. Resulting summary quantities includedn = 11, E(speed) = 205.5, E(speed)2 = 3884.08, E(rate) = 35.15, E(rate)2 = 112.691, and E(speed)(rate) = 660.136. (a) Calculate the equation of the least squares line that you would use to predict stride rate from speed. (Round all numerical values to four decimal places.) (b) Calculate the equation of the least squares line that you would use to predict speed from stride rate. (Round all numerical values to four decimal places.) (c) Calculate the coefficient of determination for the regression of stride rate on speed of part (a) and for the regression of speed on stride rate of part (b). (Round your answers to three decimal places.) for part (a) for part (b)
4.) (For Marketing & Sales Analysts-Consultants). Four months after the deliveries of goods were affected by the granular lockdown due to the Covid-19 pandemic, a manufacturer noticed that sales had dropped from 100,000 units per month to 80,000 units. If the sales follow an exponential pattern decline, what will they be after another 4 months? Note: Use the exponential model, y= Cekt, where t is measured in months.
If an error of 1 percent is made in measuring the edge of a cube, what is the percentage error in the computed volume? (SOLVE BY USING DIFFERENTIAL EQUATIONS)
38. Given the power regression model y = 40x^1.3, which is the linear regression model after transforming to a log-log graph? Y = 1.3X + 1.60 Y = 0.20X + 0.11 Y = 0.20X + 0.36 Y = 1.60X + 0.11
Log(Wagei) = α + β1Educationi + β2Femalei + β3Non Whitei + β4Educationi × Femalei + εi For males, and holding other variables constant, the regression output from the linear regression model above implies that an extra year of education is associated with what percent change in wages?
7 In a G/G/3 system with average service time equal to 6.9 minutes, average time in system equal to 25.1 minutes, what is the average wait in queue?
10. Suppose a stone is dropped from the observation deck of the Space Needle in Seattle, 160 meters above the ground. How long will it take for the stone to hit the ground? (You will need to know that the acceleration of gravity is a = -9.8 meters per second?.)

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