Suppose the population of the world was about 6.2 billion in 2000. Birth rates around that time ranged from 35 to 40 million per year and death rates ranged from 15 to 20 million per year. Let's assume that the carrying capacity for world population is 20 billion.(a) Write the logistic differential equation for these data. (Because the initial population is small compared to the carrying capacity, you can take k to be an estimate of the initial relative growth rate. Calculate k using the maximum birth rate and maximum death rate. Let t = 0 correspond to the year2000.)dt(b) Use the logistic model to estimate the world population (in billions) in the year 2010. (Round your answer to the nearest hundredth.)billionCompare this result with the actual population of 6.9 billion.This result ---Select---✓the actual population of 6.9 billion.(c) Use the logistic model to predict the world population (in billions) the years 2100 and 2400. (Round your answers to the nearest hundredth.)billionbillion21002400

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Answered: Suppose the population of the world was…

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
1. World Wildlife fund (WFO) releases 25 Leopar... Start your trialnow! First week only $4.99! Want to se 1. World Wildlife fund (WFO) releases 25 Leopards into a game preserve in Kyrgyzstan. After 2 years, there are 39 leopards in the preserve. The WFO game preserve park in Kyrgyzstan has a carrying capacity of 200 panthers. a. Write a logistic equation that models the population of leopard in the preserve. b. Find the population after 5 years. When will the population reach 100? d. Write a logistic differential equation that models the growth rate of the leopard population. At what time is the leopard population growing most rapidly? Explain. C. e. Cookies and Personal Information This site uses cookies to improve performance, personalize your experience, analyze usage and assist our marketing efforts, but we don't sell your personal data as defined in the CA Consumer Privacy Act. To opt of the use of third-party targeting cookies, check "Do Not Sell My Personal Information" and then…
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Suppose that in a logistic model the percentage growth rate G per year (in decimal form) as a function of N declines from G = 0.12 when N = 0 to G = 0 when N= 366. (a) What is the r value? r = (b) What is the carrying capacity? K = (c) At what value of N will there be a maximum growth rate? N = | Need Help? Read It
Assume that the population of a town can be modeled by the logistic equation dP/dt = kP(1000 - P). If this town's population was 800 five years ago and is 850 this year, what is its population expected to be five years from now? Round your answer to the nearest integer.
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.
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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.
Assuming a carrying capacity for world population K = 15 billion, and a population of 7.75 billion as of 2020, estimate the year when population will reach 12 billion, assuming a logistic growth curve applies and with a current growth rate ro = 1.1% per year. What will the updated growth rate rf be in that future year when population reaches 12 billion?
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A nation's population (to the nearest million) was 281 million in 2000 and 311 in 2010. It is projected that the population in 2050 will be 439 million. To construct a logistic model, both the growth rate and the carrying capacity must be estimated. There are several ways to estimate these parameters. Use parts (a) through (f) to use one approach. a. Assume that t = 0 corresponds to 2000 and that the population growth is exponential for the first ten years; that is, between 2000 and 2010, the population is given by P(t) = P(0) e". Estimate the growth rate r using this assumption. = (Round to five decimal places as needed.) b. Write the solution of the logistic equation with the value of r found in part (a). Write any populations in the logistic equation in millions of people. P(t) = Use the projected value P(50) = 439 million to find a value of the carrying capacity K. K= (Type an integer or decimal rounded to the nearest hundredth as needed.) c. According to the logistic model…
Nitrogen dioxide, NO₂, is an air pollutant resulting from burning fossil fuels in cars and power plants. The following table shows the decrease in the national average of the concentration in parts per billion (ppb) of NO₂ for selected years. Year 2014 40.8107 2015 2016 2017 2018 39.7886 38.7972 37.8209 36.8752 NO₂ (ppb) Use exponential regression to find an exponential decay function for the concentration, C, of NO₂ t years after 2014. Round constants to the nearest ten-thousandth. c-40.8114 (0.9750) Use the model to predict the concentration of NO₂ (in ppb) in 2045. Round to the nearest whole number. 21 x ppb

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