A cup of coffee is taken out of a microwave oven and placed in a room. The temperature, T , in degree Fahrenheit, of the coffee after t minutes is modeled by the function T = 70 + 130 e − 0.04355 t . The graph of the function is shown in the figure. Use the graph to answer each of the following questions, a. What was the temperature of the coffee when it was first taken out of the microwave? b. What is a reasonable estimate of the temperature of the coffee after 20 minutes? Use your calculator to verify this estimate. c. What is the limit of the temperature to which the coffee will cool? What does this tell you about the temperature of the room?
A cup of coffee is taken out of a microwave oven and placed in a room. The temperature, T , in degree Fahrenheit, of the coffee after t minutes is modeled by the function T = 70 + 130 e − 0.04355 t . The graph of the function is shown in the figure. Use the graph to answer each of the following questions, a. What was the temperature of the coffee when it was first taken out of the microwave? b. What is a reasonable estimate of the temperature of the coffee after 20 minutes? Use your calculator to verify this estimate. c. What is the limit of the temperature to which the coffee will cool? What does this tell you about the temperature of the room?
Solution Summary: The author analyzes the function T=70+130e-0.04855t to determine the temperature of coffee at the time it was taken out of the microwave.
A cup of coffee is taken out of a microwave oven and placed in a room. The temperature, T, in degree Fahrenheit, of the coffee after t minutes is modeled by the function
T
=
70
+
130
e
−
0.04355
t
. The graph of the function is shown in the figure.
Use the graph to answer each of the following questions,
a. What was the temperature of the coffee when it was first taken out of the microwave?
b. What is a reasonable estimate of the temperature of the coffee after 20 minutes? Use your calculator to verify this estimate.
c. What is the limit of the temperature to which the coffee will cool? What does this tell you about the temperature of the room?
Car A starts from rest at t = 0 and travels along a straight road with a constant acceleration of 6 ft/s^2 until it reaches a speed of 60ft/s. Afterwards it maintains the speed. Also, when t = 0, car B located 6000 ft down the road is traveling towards A at a constant speed of 80 ft/s. Determine the distance traveled by Car A when they pass each other.Write the solution using pen and draw the graph if needed.
The velocity of a particle moves along the x-axis and is given by the equation ds/dt = 40 - 3t^2 m/s. Calculate the acceleration at time t=2 s and t=4 s. Calculate also the total displacement at the given interval. Assume at t=0 s=5m.Write the solution using pen and draw the graph if needed.
The velocity of a particle moves along the x-axis and is given by the equation ds/dt = 40 - 3t^2 m/s. Calculate the acceleration at time t=2 s and t=4 s. Calculate also the total displacement at the given interval. Assume at t=0 s=5m.Write the solution using pen and draw the graph if needed.
Chapter 3 Solutions
Precalculus, Books A La Carte Edition Plus MyLab Math with eText -- Access Card Package (6th Edition)
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, calculus and related others by exploring similar questions and additional content below.
01 - What Is A Differential Equation in Calculus? Learn to Solve Ordinary Differential Equations.; Author: Math and Science;https://www.youtube.com/watch?v=K80YEHQpx9g;License: Standard YouTube License, CC-BY
Higher Order Differential Equation with constant coefficient (GATE) (Part 1) l GATE 2018; Author: GATE Lectures by Dishank;https://www.youtube.com/watch?v=ODxP7BbqAjA;License: Standard YouTube License, CC-BY