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c. Suppose you are done making a soup. It was too hot and after checking the temperature you realized that it was about 100°C. You decide to let it cool in your dining room with temperature 25°C. The Newton's law of Cooling states that the rate of cooling of an object is proportional to the temperature difference between the object and its surroundings, provided that this difference is not too large. Let T(t) represents the temperature of a bowl of soup set out in the dining room every minute. (i) (ii) (iii) dT dt dT dt dT dt = 100k(T - 25) = k(T – 25) = kT - 100

c. Suppose you are done making a soup. It was too hot and after checking the temperature you realized that it was about 100°C. You decide to let it cool in your dining room with temperature 25°C. The Newton's law of Cooling states that the rate of cooling of an object is proportional to the temperature difference between the object and its surroundings, provided that this difference is not too large. Let T(t) represents the temperature of a bowl of soup set out in the dining room every minute. (i) (ii) (iii) dT dt dT dt dT dt = 100k(T - 25) = k(T – 25) = kT - 100

Advanced Engineering Mathematics
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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Question 3 Each scenario below describes a situation which can be modeled by a differential equation. Do the following for each scenario: 1. Choose the correct equation. 2. Show and explain your reasoning for your choice.

c. Suppose you are done making a soup. It was too hot and after checking the temperature you realized that it was about 100°C. You decide to let it cool in your dining room with temperature 25°C. The Newton's law of Cooling states that the rate of cooling of an object is proportional to the temperature difference between the object and its surroundings, provided that this difference is not too large. Let T(t) represents the temperature of a bowl of soup set out in the dining room every minute. (i) (ii) (iii) dT dt dT dt dT dt = 100k (T25) - = k(T - 25) = kT-100
Transcribed Image Text:c. Suppose you are done making a soup. It was too hot and after checking the temperature you realized that it was about 100°C. You decide to let it cool in your dining room with temperature 25°C. The Newton's law of Cooling states that the rate of cooling of an object is proportional to the temperature difference between the object and its surroundings, provided that this difference is not too large. Let T(t) represents the temperature of a bowl of soup set out in the dining room every minute. (i) (ii) (iii) dT dt dT dt dT dt = 100k (T25) - = k(T - 25) = kT-100
a. A biologist is making a bacteria culture starting with 100 cells in a petri dish. The biologist is recording the number of bacteria every hour. Let N(t) be the number of bacteria in the petri dish after t hours. After many recording the biologist finds that the change in the number of bacteria is proportional to the square of the number of bacteria present at the time of recording. (i) dN dt € dN dt dN dt ds dt b. A youtuber decides to analyze her subscribers growth. Let S(t) be the number of sub- scribers after t months. Using an analysis software, she notices that the change in the number of subscribers is proportional to the square root of the age (in months) of her account. Note that when her account was 9 months old her subscribers had increased by 300. (i) dS dt = k(100 – N)² ds dt = k(N² – 100) = kN² = 100√t 3000√t = k√(t+300) c. Suppose you are done making a soup. It was too hot and after checking the temperature you realized that it was about 100°C. You decide to let it cool in your dining room with temperature 25°C. The Newton's law of Cooling states that the rate of cooling of an object is proportional to the temperature difference between the object and its surroundings, provided that this difference is not too large. Let T(t) represents the temperature of a bowl of soup set out in the dining room every minute.
Transcribed Image Text:a. A biologist is making a bacteria culture starting with 100 cells in a petri dish. The biologist is recording the number of bacteria every hour. Let N(t) be the number of bacteria in the petri dish after t hours. After many recording the biologist finds that the change in the number of bacteria is proportional to the square of the number of bacteria present at the time of recording. (i) dN dt € dN dt dN dt ds dt b. A youtuber decides to analyze her subscribers growth. Let S(t) be the number of sub- scribers after t months. Using an analysis software, she notices that the change in the number of subscribers is proportional to the square root of the age (in months) of her account. Note that when her account was 9 months old her subscribers had increased by 300. (i) dS dt = k(100 – N)² ds dt = k(N² – 100) = kN² = 100√t 3000√t = k√(t+300) c. Suppose you are done making a soup. It was too hot and after checking the temperature you realized that it was about 100°C. You decide to let it cool in your dining room with temperature 25°C. The Newton's law of Cooling states that the rate of cooling of an object is proportional to the temperature difference between the object and its surroundings, provided that this difference is not too large. Let T(t) represents the temperature of a bowl of soup set out in the dining room every minute.
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