According to a recent data analysis, the amount A(t) of atmospheric pollutants in a certain city is found toapproximately quadruple every 9.5 years. The current amount of pollution in this city is 25 pu (pollutant units), and it isconsidered to be dangerous to stay in the city when the amount of pollutants reaches 120 pu.Applying the differential equation model: (dA/dt) = kA, (k>0)approximately, how long do the residents of this city have before the dangerous limit is reached?Choose all correct answers.A Less than 12 years.BMore than 9 years.Less than 10 years.More than 11 years.

Answered: Image /qna-images/answer/7d131274-38f0-45bd-97f4-d64362aee4ce.jpg

Answered: ccording to a recent data analysis, 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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The half-life of a radioactive element is the number of years it takes for an observed amount of that element to decay or degrade to another element. Suppose that an element decays according to the radioactive decay model. dA/dt = kA Then the half-life T is given by:
The table shows the yield (in bushels per acre) and the total production (in millions of bushels) for com in a country for selected years since 1950. Let x represent years since 1900. Find a logarithmic regression model (y = a +b In x) for the yield. Estimate the yield in 2023. The regression model is y=+Inx (Round to one decimal place as needed.) The estimated yield in 2023 is bushels/acre (Round to the nearest integer) GOOOD Year 1950 1960 1970 1980 1990 2000 2010 *8828889 50 60 100 110 Yield 41 57 83 93 116 142 154 C
True or false: If the regression equation ln(Qx)=b + BTime + e is estimated using daily data, then the constant weekly percentage growth rate is g=eB-1
The table below represents the number of clients for a company from 2018 to 2022 (t − 0 represents 2018): Year, t Clients(Thousands) 1 6 2 10 3 25 4 34 (a) Find a logarithmic regression model, f(t) = A ln t + C to represent the data. (b) Using the model, predict the number of users in 2023? (c) Using the model, when will the company exceed 5227 clients?
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The concentration of DDT (dichlorodiphenyltrichloroethane) in Lake Erie has been declining exponentially over the last several decades. In 1970, the DDT concentration was 13.59 ppm (parts per million). In 1985, the DDT concentration was 2.37 ppm. Part 1. Using these data points, determine the exponential decay function to model the DDT concentration decline in terms of years, tt, where t=0 represents the year 1970. (Round values to 4 decimal places) Part 2.
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?
During the period from 1790 to 1930, a country's population P(t) (t in years) grew from 3.7 million to 118.6 million. Throughout this period, P(t) remained close to the solution of the initial value dP problem = 0.03145P-0.0001486P², P(0) = 3.7. dt (a) What 1930 population does this logistic equation predict? (b) What limiting population does it predict? (c) The country's population in 2000 was 350 million. Has this logistic equation continued since 1930 to accurately model the country's population?
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