If is the size of a population at time
, which of the following differential equations describes linear growth in the size of the population?
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First-Order Differential Equations
If is the size of a population at time
, which of the following differential equations describes linear growth in the size of the population?
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If is the size of a population at time
, which of the following differential equations describes exponential growth in the size of the population?
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The rate of change of the volume, , of oil in a tank with respect to time,
, is directly proportional to the cube root of the volume. Which of the following is a differential equation that describes this relationship?
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Which of the following is the solution to the differential equation with the initial condition
?
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Which of the following is the solution to the differential equation with the initial condition
?
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Let be the solution to the differential equation
with initial condition
. What is the approximation for
obtained by using Euler's method with a step size of
starting at
?
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Which of the following is a logistic differential equation?
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A disease spreads among a population of people at a rate which is proportional to the product of the number of people infected by the disease and the number of people not infected by the disease. If
denotes the number of people infected by the disease, which of the following differential equations could be used to model this situation with respect to time,
, where
is a positive constant.
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If satisfies
, where
is a non-zero constant, then
could be
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The slope field shown above corresponds to which of the following differential equations?
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Which of the following is the solution to the differential equation with the initial condition
?
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If satisfies
, then
could be
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Let be the solution to the differential equation
with initial condition
. What is the approximation for
obtained by using Euler's method with two steps of equal length starting at
?
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The population of a species satisfies the logistic differential equation
. What is the carrying capacity of the system modeled by the equation?
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The growth of population is described by the differential equation
, where
is a constant and
is measured in hours. If the population doubles every 8 hours, then the value of
is
0.087
0.250
0.271
4.351
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Which of the following is the solution to the differential equation with the initial condition
?
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Shown above is a slope field for which of the following differential equations?
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In the differential equation ,
is a positive integer. Which of the following is the solution to the differential equation with the initial condition
?
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The number of radioactive atoms, , in a sample is described by the differential equation
, where
is a positive constant and
is measured in years. If the number of radioactive atoms is only one tenth of the original number after 1.255 years, then the value of
is
0.545
1.290
1.835
2.380
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Consider the differential equation . Let
be a particular solution to the differential equation with the initial equation
, where
is a constant. Euler's method, starting at
with a step size of
, gives the approximation
. What is the value of
?
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The population of a species of predator satisfies the differential equation
, where the initial population is
and time
is measured in years. What is
as predicted by the model?
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