(c) Use Euler's method with step size h= 1 to estimate the population after 50 years if the initial population is 1,000. (Round your answer to the nearest whole number.)P(50) -(d) If the initial population is 1,000, write a formula for the population after t years. (Use P for P(t).)57001+4.9e-0.0016 XP=Use it to find the population after 50 years and compare with your estimate in part (c). (Round your answer to one decimal place.)P(50) - Suppose that a population grows according to a logistic model with carrying capacity 5700 and k = 0.0016 per year.(a) Write the logistic differential equation for these values.0.0016P(1-dPdt-5700

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Answered: Suppose that a population grows…

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 scientist develops the logistic population model P' 0.2P(1) to describe her research data. This model has an equilibrium value of P = 8. In this model, from the initial condition Po = 4, the population will never reach the equilibrium value because: (a) the population will grow toward infinity (b) the population is asymptotically approaching a value of 8. (c) the population will drop to 0 Briefly describe how you determined your answer.
Assume there is a certain population of fish in a pond whose growth is described by the logistic equation. The growth parameter for this type of fish is r = 3.0. The logistic growth formula is given by PN+1 rPN(1-PN) If originally the pond is stocked to 50% of its carrying capacity, then the population of the pond after the second breeding season is Select one: a. 25% of the pond's carrying capacity. b. 56.25% of the pond's carrying capacity. c. 75% of the pond's carrying capacity. d. none of these O e. 50% of the pond's carrying capacity.
Suppose the population of a species of animals on an island is governed by the logistic model with relative rate of growth k = 0.05 and carrying capacity M= 15000. I.e., the population function P(t) satisfies the equation P' = bP(15000 - P), where b = k/M. If the current population is P(0) = 20000, which one of the following is closest to P(1)? O a) 19700 O b) 19890 Oc) 19680 Od) 19690 Oe) 19805 Of) 19742 Motion
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
Assume there is a certain population of fish in a pond whose growth is described by the logistic equation. It is estimated that the carrying capacity for the pond is 1000 fish. Absent constraints, the population would grow by 190% per year.If the starting population is given by �0=300, then after one breeding season the population of the pond is given by�1 = After two breeding seasons the population of the pond is given by�2 =
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?
Biologists stocked a lake with 300 fish and estimated the carrying capacity (the maximal population for the fish of that species in that lake) to be 5000. The number of fish tripled in the first year. (a) Assuming that the size of the fish population satisfies the logistic equation dP = kp (1-P). (1-²), kP dt determine the constant k, and then solve the equation to find an expression for the size of the population after t years. k= P(t)= (b) How long will it take for the population to increase to 2500 (half of the carrying capacity)? It will take years.
Assume there is a certain population of fish in a pond whose growth is described by the logistic equation. It is estimated that the carrying capacity for the pond is 2000 fish. Absent constraints, the population would grow by 190% per year.If the starting population is given by �0=500, then after one breeding season the population of the pond is given by�1 = After two breeding seasons the population of the pond is given by�2 =
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?
Assume there is a certain population of fish in a pond whose growth is described by the logistic equation. It is estimated that the carrying capacity for the pond is 1200 fish. Absent constraints, the population would grow by 110% per year.If the starting population is given by �0=500, then after one breeding season the population of the pond is given by�1 = After two breeding seasons the population of the pond is given by�2 =
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 -0.0001494P² P(0) = 3.6. dP dt = 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 accurately model the country's population? (a) The logistic equation predicts the population in 1920 to be million. (Do not round until the final answer. Then round to the nearest thousandth as needed.) K AI C H TU U →> C ¢ ➡ H i O + 2.4 e В → نه Y + - 8 .... : *** 5 Ø Co Less . N 0 .. H A E X U i 9 A C ש Σ VI 8 FR > in X
Suppose that P, is invested in a savings account in which interest is compounded continuously at 5.2% per year. That is, the balance P grows at the rate given by P = .052 P(t) dt a) Find the function P(t) that satisfies the equation. b) Suppose that $1200 is invested. What is the balance after 4 years? c) When will an investment of $1800 double itself?

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Suppose that a population grows according to a logistic model with carrying capacity 5700 and k = 0.0016 per year. (a) Write the logistic differential equation for these values. 0.0016P(1-5700) dp dt