2. If one denotes the population of a planet by E(t) per year t, then the populationgrowth rate dE/dt is characterized bydEdt= kE,wherek denotes the constant of proportionality.(a) Find an exact expression for k given that the population E of the planet doublesevery 37 years.(b) The population of this city is initially 300, 000. How many years (T) would it takefor the population to grow to 10, 000, 000? Give your answer to the nearest year.

Answered: Image /qna-images/answer/379b01d7-0221-4407-90b8-21892bac4c2f.jpg

Answered: 2. If one denotes the population of 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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Q No. 2: Five people in a community with stable population of 5000 people got infected with a contagious disease (such as covid 19). A theory of epidemic spread postulates that the rate of change in the infected population (number of people) is proportional to the product of the number of people who have the disease with the number that are disease free (take the constant of proportionality as 6.0 x 104). Assuming the theory is correct, how long will it take 75% of the population to contract the disease? (Assume the community as a closed system with nobody goes out or comes in but they are free to meet each other).
Evaluate:
The half life of substance A is 22 years, and substance B decays at a rate of 30 each decade. (a) Find a formula for a function f(t) that gives the amount of substance A, in milligrams, left after t years, given that the initial quantity was 100 milligrams. f(t) = help (formulas) (a) Find a formula for a function g(t) that gives the amount of substance B, in milligrams, left after t years, given that the initial quantity was 100 milligrams. g(t) help (formulas) (c) of which substance is there less in the long term? OA. There is less of substance B in the long term. OB. There is less of substance A in the long term. OC. There is no way to tell.
At what speed should a fish swim upstream so as to reach its destination with the least expenditure of energy? The energy depends on the friction of the fish through the water and on the duration of the trip. If the fish swims with velocity v, the energy has been found experimentally to be proportional to (for constant k > 2) times the duration of the trip. A distance of s miles against a current of speed c requires time -c (distance divided by speed). The energy required is then proportional to k = 3, minimizing energy is equivalent to minimizing |- v³ E(v) = = V C vk s v-c. For Find the speed v with which the fish should swim in order to minimize its expenditure E(v). (Your answer will depend on c, the speed of the current.)
Kleiber's Law states that the metabolic needs (such as calorie requirements) of a mammal are proportional to its body weight raised to the 0.75 power.¹ Surprisingly, the daily diets of mammals conform to this relation well. Assuming Kleiber's Law holds, answer the following questions. (a) Write a formula for C, daily calorie consumption, as a function of body weight, W. NOTE: Use k for the constant of proportionality. C(W) = (b) If a human weighing 150 pounds needs to consume 1800 calories a day, estimate the daily calorie requirement of a horse weighing 740 lbs and of a rabbit weighing 11 lbs. NOTE: Round your answers to the nearest calorie. Daily calorie requirement of a horse = Daily calorie requirement of a rabbit = calories Choose one calories (c) On a per-pound basis, which animal requires more calories: a mouse or an elephant? ¹S. Strogatz. "Math and the City." The New York Times. May 20, 2009. Kleiber originally
The population of Normal, Illinois grows proportionally to its population at time t. At an initial population of 2100, it grows at a rate of 8% over 10 years. What is the value of the proportionality constant?
1. A team of biologists stocked a lake with 100 fish of one species to conduct an experiment. They concluded that the rate of increase of the fish population is directly proportional to the population at that time, p(t) as well as to the difference between species' carrying capacity and the current population. The carrying capacity for this fish species in the lake was estimated to be 1000. It was observed that the number of the fish tripled in the first year. What would be the fish population in 5 years?

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