3Questiond'The rate of change, dp, of the number of people entering a movie theater is modeled by a logistic differential equation. The capacity of the theater is 500 people. At a certain time, the number of people in thetheater is 100 and is increasing at the rate of 50 per minute. Which of the following differential equations could describe this situation?(500-P)A(ВBCDP=dtdPdt= ¹P (500 - P)50dPdt800P (500-P)= P (500+ P)1200Type here to search2AxF2#3F3O4)$4F4DII%5FS•*F6A646OF7&7PrtScnF88HomeF9924°FEndF10D GPgUp.F110AXPgDnF1212:22 PM2/24/2023Q?DĘIns

Answered: Image /qna-images/answer/e9bac193-df0d-4f07-8a4b-c08e4d747b92.jpg

Answered: The rate of change, de, of the number…

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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A strain of bacteria has a growth rate that is proportional to the size of the population. Initially, there are 100 bacteria; after 3 hours, there are 1600. (a) If p(t) denotes the number of bacteria after t hours, find a formula for p(t). (b) How long does it take for the population to double? (c) When will the population reach one million?
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
9. Solve the following simultaneous equations: logx+log(y²)=4 log²x-3log(xy) = -5 Where x, y are real numbers
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?
Due to the rising temperatures in a bay ecosystem, the population mass of a certain species of jellyfish is growing exponentially. When first measured in 2010 (which we can call year t = 0), the bay contained about 600 tons of jellyfish. Now in 2021 (t = 11), the bay has 2,000 tons. If it continues to grow in this way, in what year will the jellyfish population mass reach 10,000 tons?
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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