6 Questions
What is the general form of a differential equation that models the growth of a population that doubles every hour?
dy/dt = ky, where k is a constant
What is the particular solution to the differential equation dy/dt = 2y with the initial condition y(0) = 5?
y = 5e^(2t)
What is the general form of a separable differential equation?
dy/dt = f(y)g(t)
What is the half-life of a radioactive substance that decays at a rate proportional to its mass?
The half-life is the time it takes for the mass to decrease by half, given by the formula t_half = ln(2) / k, where k is the decay rate.
What is the formula for the volume of a solid generated by revolving a region around the x-axis?
V = π ∫[a, b] (f(x))^2 dx
What is the shape of the cross section of a solid formed by revolving the region between y = √x and y = x about the y-axis?
A washer
Test your skills in modeling population growth, finding particular solutions, and solving separable differential equations. Take this quiz to see how well you can apply differential equations to real-world problems.
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