During the period from 1790 to 1920, a country's population P(t) (t in years) grew from 3.6 million to 101.6 million.Throughout this period, P(t) remained close to the solution of the initial value problem-0.0001494P²P(0) = 3.6.dPdt= 0.03136P-((a) What 1920 population does this logistic equation predict?(b) What limiting population does it predict?(c) The country's population in 2000 was 259 million. Has this logistic equation continued since 1920 to accuratelymodel the country's population?(a) The logistic equation predicts the population in 1920 to be million. (Do not round until the final answer. Thenround to the nearest thousandth as needed.)KAICHTUU→>C¢➡HiO+2.4eВ→نهY+-8....:***5ØCoLess.N0..HAEXUi9ACשΣVI8FR>inX

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Answered: During the period from 1790 to 1920, a…

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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For a Pacific halibut population, the value of r is 0.71 per year, and the environmental carrying capacity is 89 thousand tons of fish.† (a) Find the time it takes the population to grow from the optimum yield level to 87% of carrying capacity if the number b in the logistic growth equation is 1.5. (Round your answer to three decimal places.) yr(b) Find the time it takes the population to grow from the optimum yield level to 87% of carrying capacity if the number b in the logistic growth equation is 4.8. (Round your answer to three decimal places.) yr
A population grows according to the logistic growth model, with growth parameter r= 1.8. Starting with an initial population given by P = 0.6, complete parts (a) and (b). (a) Find the values of p₁ through P10- P₁ = ₁ P₂ = P3 = P4 = P5 P10 = P6= P7 = ₁ P8 = Pg = ₁ (Round to four decimal places as needed.) (b) What does the logistic model predict in the long term for this population? O A. The population settles into a two-period cycle with the following approximate percentages of the habitat's carrying capacity: 44.17% and 44.43%. OB. It stabilizes at about 44.44% of the habitat's carrying capacity. C. The species will become extinct. OD. The population settles into a four-period cycle with the following approximate percentages of the habitat's carrying capacity: 44.17%, 44.43%, 43.20%, 44.44%.
Hello! How do you solve part (a), (b), and (c) of the question attached below? Thank you for your help! Have a nice day :)
At time t = 0, a bacterial culture weighs 2 grams. Three hours later, the culture weighs 5 grams. The maximum weight of the culture is 20 grams. (a) Write a logistic equation that models the weight of the bacterial culture. (Round your coefficients to four decimal places.) 20 y = dy dt = 1 +9e 8 g (c) When will the culture's weight reach 16 grams? (Round your answer to two decimal places.) 9.79 hr (d) Write a logistic differential equation that models the growth rate of the culture's weight. Then repeat part (b) using Euler's Method with a step size of h = 1. (Round your answer to the nearest whole number.) y(5) = 6 -0.3662t = 1.37 0.366y| 1 (1-20) (b) Find the culture's weight after 5 hours. (Round your answer to the nearest whole number.) X g (e) At what time is the culture's weight increasing most rapidly? (Round your answer to two decimal places.) hr
A study of Maryland's portion of Chesapeake Bay found the following information about stocks of market-sized oysters.† In 1994, the stocks were 218 million. (This is the number you will use for the initial population N(0).) The carrying capacity is 5089 million oysters. The intrinsic exponential growth rate is 0.274 per year. (a) Find a logistic model N(t) for the number, in millions, of market-sized oysters. Take t to be the time in years since 1994. (Rround all regression parameters to three decimal places.) N(t) = (b) Plot the graph of the model you found in part (a) over the first 20 years. (c) How many market-sized oysters does your model predict for 2007? Round your answer, in millions, to the nearest whole number. million oysters (d) The actual number of market-sized oysters was found to be 82 million. Use the Internet to find possible explanations for the reduced levels of oysters in Chesapeake Bay.
The population, P, of kangaroos in a reservation is modelled by the logistic dP equation = dt 2P (5- reservation. - P 10 000 ) where t is measured in days. It is estimated that initially the population of the kangaroos is 15% of the carrying capacity of the (i) What is the initial population of the kangaroos? (ii) What is the population of the kangaroos when the rate of increase is a maximum?
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?
One of the main contaminants of a nuclear accident, such as that at Chernobyl, is strontium-90, which decays exponentially at a rate of approximately 2.4% per year. (a) Write the percent of strontium-90 remaining, P, as a function of years, t, since the nuclear accident. [Hint: 100% of the contaminant remains at t = 0.] P(t)= = (b) Estimate the half-life of strontium-90. NOTE: Round your answer to the nearest integer. The half-life of strontium-90 is (c) After the Chernobyl disaster, it was predicted that the region would not be safe for human habitation for 100 years. Estimate the percent of original strontium-90 remaining at this time. NOTE: Round your answer to the nearest integer. There is about of original strontium-90 remaining at this time. years. %

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