The population size x(t)in the logistic equationdxx(1 – 0.5x)dtis evaluated from the equation2x(t)ce-t +1(a) Find all the value(s) of c when the initialpopulation is x(0) = 0.5(b) Evaluate the population after 2 years with thevalue of c found in Part (a).%3D

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Answered: The population size x(t) in the…

Calculus: Early Transcendentals

8th Edition

ISBN:9781285741550

Author:James Stewart

Publisher:James Stewart

Chapter1: Functions And Models

Section: Chapter Questions

Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...

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The population of an aquatic species in a certain body of water is approximated by the logistic function 37,500 where t is measured in years. Find G(t) = = ,-0.56t' the population and its growth rate at the following times. a. 1 year b. 5 years c. 12 years d. What happens to the rate of growth over time? 1 + 12e The population in 1 year is 4774 . (Round to the nearest whole number.) The population in 5 years is 21680. (Round to the nearest whole number.) The population in 12 years is 36965. (Round to the nearest whole number.) The growth rate in 1 year is per year. (Round to the nearest whole number.)
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?
(a) Solve the logistic equation y' = 0.27 - 0.005y2 , y(0) = 50. (b) What is the limiting value yL. (c) How long a time will it take to reach 110% yL?
Parent Function y = log10x (x, y) VA x = Transformed Function y = -2log10 (x + 4) - 3 VA x =
log(salary) = 8.34 + 0.0047LSAT + 0.248GPA + 0.095log(libvol) + 0.038log(cost) + 0.0033rank 1+ ɛ 136, R2: = 0.842 n = What is the predicted ceteris paribus difference in salary for institutions with a median GPA different by one point? (Report your answer as a percentage.)
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

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The population size x(t) in the logistic equation dx x(1 – 0.5x) dt is evaluated from the equation x(t) = се1 + 1 (a) Find all the value(s) of c when the initial population is x(0) = 0.5 (b) Evaluate the population after 2 years with the value of c found in Part (a).