0.349 A hard-boiled egg is removed from a pot of hot water and set on the table to cool. The rate of change of the egg's temperature T with respect to time t is proportional to the difference between the egg's temperature in degrees Fahrenheit (°F) and the room temperature of 75°F. Which of the following is a differential equation that describes this relationship, where k is a constant? Which of the following could be a slope field for the differential equation dydx=y3−x ? Let y=f(x) be the particular solution to the differential equation dydx=ex−1ey with the initial condition f(1)=0. What is the value of f(−2) ? Out of a total of N students at a school, the number of students who have seen a new television program increases at a rate proportional to the product of the number of students who have seen the program and the number of students who have not seen the program. If S denotes the number of students who have seen the program at time t, which of the following differential equations could be used to model this situation, where k is a positive constant?

Let y=f(x) be the particular solution to the differential equation dydx=ex−1ey with the initial condition f(1)=0. What is the value of f(−2) ?

dV/dt=−0.2V^3 Let y=f(x) be the particular solution to the differential equation dy/dx=3x^2−1/2y with the initial condition f(1)=4. Which of the following is an expression for f(x) ? What is the general solution to the differential equation dy/dx=cos(8x)/cos(4y) ? The rate of change of the volume V with respect to time t of water leaking from a tank is proportional to the cube of the volume. Which of the following is a differential equation that could describe this relationship? The amount of bacteria in a petri dish increases at a rate proportional to the amount present. At time t=0, the amount of bacteria in the dish is 10 grams. At time t=2, the amount of bacteria in the dish is 30 grams. What is the amount of bacteria in the dish at time t=6 ?

The rate of change of the volume V with respect to time t of water leaking from a tank is proportional to the cube of the volume. Which of the following is a differential equation that could describe this relationship?

dT/dt=k(T−75) A hard-boiled egg is removed from a pot of hot water and set on the table to cool. The rate of change of the egg's temperature T with respect to time t is proportional to the difference between the egg's temperature in degrees Fahrenheit (°F) and the room temperature of 75°F. Which of the following is a differential equation that describes this relationship, where k is a constant? Which of the following is a solution to the differential equation xy′−3y=6 ? Let y=f(x) be the particular solution to the differential equation dy/dx=3x^2−1/2y with the initial condition f(1)=4. Which of the following is an expression for f(x) ? Which of the following is the particular solution to the differential equation dy/dx=sin(x^2) with the initial condition y(√π)=4 ?

A hard-boiled egg is removed from a pot of hot water and set on the table to cool. The rate of change of the egg's temperature T with respect to time t is proportional to the difference between the egg's temperature in degrees Fahrenheit (°F) and the room temperature of 75°F. Which of the following is a differential equation that describes this relationship, where k is a constant?

dS/dt=kS(N−S) Let y=f(x) be the particular solution to the differential equation dy/dx=2x−1/y^2 with the initial condition y(0)=3. Which of the following is an expression for f(x) ? Out of a total of N students at a school, the number of students who have seen a new television program increases at a rate proportional to the product of the number of students who have seen the program and the number of students who have not seen the program. If S denotes the number of students who have seen the program at time t, which of the following differential equations could be used to model this situation, where k is a positive constant? Which of the following is a solution to the differential equation xy′−3y=6 ? Let y=f(x) be the particular solution to the differential equation dydx=ex−1ey with the initial condition f(1)=0. What is the value of f(−2) ?

Out of a total of N students at a school, the number of students who have seen a new television program increases at a rate proportional to the product of the number of students who have seen the program and the number of students who have not seen the program. If S denotes the number of students who have seen the program at time t, which of the following differential equations could be used to model this situation, where k is a positive constant?