**Newton's Law of Cooling Exercise**A graphing calculator is recommended for this exercise.**Problem Statement:**This exercise involves applying Newton's Law of Cooling.Scenario: A kettle full of water is brought to a boil in a room with a temperature of 20°C. After 15 minutes, the temperature of the water decreases from 100°C to 75°C. Determine the temperature after an additional 11 minutes. (Round your answer to one decimal place.)Output your answer in the box provided:\[ \_\_\_\_ \text{ °C} \]**Graphical Representation:**Illustrate the cooling process by graphing the temperature function. Below are four graphs that represent potential temperature functions over time $ t $:1. **Graph 1:** Displays a gradual decrease in temperature from 100°C, leveling off as time progresses.2. **Graph 2:** Also shows a decline from 100°C, with a more pronounced drop after 20 minutes. 3. **Graph 3:** Depicts a consistent decrease from 100°C without a sharp drop-off.4. **Graph 4:** Illustrates a linear decrease from 100°C over time.Each graph has axes labeled as "T" for Temperature and "t" for time (minutes). You must select the graph that accurately represents the temperature function according to Newton's Law of Cooling in this scenario. Select your choice using the radio buttons provided beneath each graph. This exercise uses Newton's Law of Cooling.Newton's Law of Cooling is used in homicide investigations to determine the time of death. The normal body temperature is 98.6°F. Immediately following death, the body begins to cool. It has been determined experimentally that the constant in Newton's Law of Cooling is approximately $ k = 0.1947 $, assuming time is measured in hours. Suppose that the temperature of the surroundings is 55°F.(a) Find a function $ T(t) $ that models the temperature $ t $ hours after death.\[ T(t) = \](b) If the temperature of the body is now 78°F, how long ago was the time of death? (Round your answer to the nearest whole number.)\[ \boxed{\phantom{00}} \] hr

By using Newton,s law of cooling:Tt=Ts+D0e-ktwherethe surround's temperature is 55°F So: Ts=55.now,…

Newton's Law of Cooling is used in homicide investigations to determine the time of death. The normal body temperature is 98.6°F. Immediately following death, the body begins to cool. It has been determined experimentally that the constant in Newton's Law of Cooling is approximately k = 0.1947, assuming time is measured in hours. Suppose that the temperature of the surroundings is 55°F. (a) Find a function T(t) that models the temperature t hours after death. T(t) = (b) If the temperature of the body is now 78°F, how long ago was the time of death? (Round your answer to the nearest whole number.) hr

Newton's Law of Cooling is used in homicide investigations to determine the time of death. The normal body temperature is 98.6°F. Immediately following death, the body begins to cool. It has been determined experimentally that the constant in Newton's Law of Cooling is approximately k = 0.1947, assuming time is measured in hours. Suppose that the temperature of the surroundings is 55°F. (a) Find a function T(t) that models the temperature t hours after death. T(t) = (b) If the temperature of the body is now 78°F, how long ago was the time of death? (Round your answer to the nearest whole number.) hr

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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Concept explainers

Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.

Question

**Newton's Law of Cooling Exercise**

A graphing calculator is recommended for this exercise.

**Problem Statement:**

This exercise involves applying Newton's Law of Cooling.

Scenario: A kettle full of water is brought to a boil in a room with a temperature of 20°C. After 15 minutes, the temperature of the water decreases from 100°C to 75°C. Determine the temperature after an additional 11 minutes. (Round your answer to one decimal place.)

Output your answer in the box provided:

\[ \_\_\_\_ \text{ °C} \]

**Graphical Representation:**

Illustrate the cooling process by graphing the temperature function. Below are four graphs that represent potential temperature functions over time $ t $:

1. **Graph 1:** Displays a gradual decrease in temperature from 100°C, leveling off as time progresses.

2. **Graph 2:** Also shows a decline from 100°C, with a more pronounced drop after 20 minutes.

3. **Graph 3:** Depicts a consistent decrease from 100°C without a sharp drop-off.

4. **Graph 4:** Illustrates a linear decrease from 100°C over time.

Each graph has axes labeled as "T" for Temperature and "t" for time (minutes). You must select the graph that accurately represents the temperature function according to Newton's Law of Cooling in this scenario.

Select your choice using the radio buttons provided beneath each graph.

This exercise uses Newton's Law of Cooling.

Newton's Law of Cooling is used in homicide investigations to determine the time of death. The normal body temperature is 98.6°F. Immediately following death, the body begins to cool. It has been determined experimentally that the constant in Newton's Law of Cooling is approximately $ k = 0.1947 $, assuming time is measured in hours. Suppose that the temperature of the surroundings is 55°F.

(a) Find a function $ T(t) $ that models the temperature $ t $ hours after death.

\[ T(t) = \]

(b) If the temperature of the body is now 78°F, how long ago was the time of death? (Round your answer to the nearest whole number.)

\[ \boxed{\phantom{00}} \] hr

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