Question 1

Find all equilibrium points for the following coupled predator-prey-model equations.

Accepted Answer

A)  (0, 0), (2.000, 0), (0.500, 0.375) 
B)  (0, 0), (0.500, 0), (2.000, 0.500) 
C)  (0, 0), (0.500, 2.000), (0, 0.375) 
D)  (0, 0), (2.000, 0), (0.500, 0.250) 
A)  (0, 0), (2.000, 0), (0.500, 0.375) 
B)  (0, 0), (0.500, 0), (2.000, 0.500) 
C)  (0, 0), (0.500, 2.000), (0, 0.375) 
D)  (0, 0), (2.000, 0), (0.500, 0.250)

Question 2

The differential equation is separable. Find the general solution in an explicit form.

Accepted Answer

A)    
B)    
C)    
D)    
A)    
B)    
C)    
D)

Question 3

Write the following third-order equation as a system of equations.

Accepted Answer

The answer of Write the following third-order equation as a...

Question 4

Calculate how much you would need to invest now in order to fund a year of college twenty years from now, assuming a year of college costs $26,000 now and is inflating at 6%, and your investment will earn 10%. Assume continuous compounding.

Accepted Answer

A)  $11,683 
B)  $3519 
C)  $7831 
D)  $57,864 
A)  $11,683 
B)  $3519 
C)  $7831 
D)  $57,864

Question 5

Identify the equilibrium solutions for   , and determine if they are stable or unstable.

Accepted Answer

A)  y =   (unstable); y =   (stable) 
B)  y =   (stable); y =   (stable) 
C)  y =   (stable); y =   (stable) 
D)  y =   (unstable); y =   (stable) 
A)  y =   (unstable); y =   (stable) 
B)  y =   (stable); y =   (stable) 
C)  y =   (stable); y =   (stable) 
D)  y =   (unstable); y =   (stable)

Question 6

Use your calculator to construct the direction field for the following differential equation. [Use the standard zoom window.]

Accepted Answer

The answer of Use your calculator to construct the direction...

Question 7

Match the appropriate slope field with the differential equation   .

Accepted Answer

A)    
B)    
C)    
D)    
A)    
B)    
C)    
D)

Question 8

Find all equilibrium points for the following coupled equations. Identify each equilibrium point as stable or unstable.

Accepted Answer

A)  (0, 0)unstable; (1.33, 1.50)stable; (0.50, 0)unstable; (0, 1.25)unstable 
B)  (0, 0)unstable; (0, 0.33)unstable; (0.50, 0)unstable; (0.50, 0.33)stable 
C)  (0, 0)unstable; (0, 0.33)unstable; (0.50, 0)unstable; (1.33, 1.50)stable 
D)  (0, 0)unstable; (0, 1.50)unstable; (1.33, 0)unstable; (0.50, 1.25)stable 
A)  (0, 0)unstable; (1.33, 1.50)stable; (0.50, 0)unstable; (0, 1.25)unstable 
B)  (0, 0)unstable; (0, 0.33)unstable; (0.50, 0)unstable; (0.50, 0.33)stable 
C)  (0, 0)unstable; (0, 0.33)unstable; (0.50, 0)unstable; (1.33, 1.50)stable 
D)  (0, 0)unstable; (0, 1.50)unstable; (1.33, 0)unstable; (0.50, 1.25)stable

Question 9

Solve the following initial value problem explicitly.

Accepted Answer

A)    
B)    
C)    
D)    
A)    
B)    
C)    
D)

Question 10

Use Euler's method with h = 0.1 to approximate y(1.0) and y(2.0) for the differential equation   ,   .

Accepted Answer

A)  -0.03685, 0.53979 
B)  -0.06263, 0.51232 
C)  -0.38500, -1.87000 
D)  0.07900, 0.55182 
A)  -0.03685, 0.53979 
B)  -0.06263, 0.51232 
C)  -0.38500, -1.87000 
D)  0.07900, 0.55182

Question 11

$50,000 that was invested in 1990 was worth $134,100 in 2000. What annual interest rate did the investment earn in that 10 year period? Assume continuous compounding.

Accepted Answer

A)  118.06% 
B)  10.91% 
C)  108.20% 
D)  9.87% 
A)  118.06% 
B)  10.91% 
C)  108.20% 
D)  9.87%

Question 12

In 1995 an investor put $2000 in an account which paid 8%. In 2005 she withdrew $1000 from the account. What will the account be worth in 2020 ?

Accepted Answer

A)  $13,778.11 
B)  $11,458.00 
C)  $7389.06 
D)  $3451.08 
A)  $13,778.11 
B)  $11,458.00 
C)  $7389.06 
D)  $3451.08

Question 13

A particular investment program involves continuously making small investments adding up to $3600 each year. If the investment pays 12%, and the account started off with an initial balance of $500, how much will the account be worth in 40 years?

Accepted Answer

A)  $3,676,068 
B)  $3,615,313 
C)  $60,755 
D)  $3,706,068 
A)  $3,676,068 
B)  $3,615,313 
C)  $60,755 
D)  $3,706,068

Question 14

Find the solution to the following separable differential equation.   , a is a constant

Accepted Answer

A)    
B)    
C)    
D)    
A)    
B)    
C)    
D)

Question 15

The conversion of sucrose (table sugar) to glucose and fructose is first order in the concentration of sucrose, which means that the rate of reaction is proportional to the concentration of the sucrose. The rate of disappearance of sucrose can be expressed as   , where c represents the concentration of the sucrose, and k is called the rate constant and is mathematically identical to the negative of the decay constant. If it takes 4 hours for the sucrose concentration to drop by a factor of 8, what is the rate constant?

Accepted Answer

A)  0.69 hour-1 
B)  0.50 hour-1 
C)  0.52 hour-1 
D)  2.00 hour-1 
A)  0.69 hour-1 
B)  0.50 hour-1 
C)  0.52 hour-1 
D)  2.00 hour-1

Question 16

The Polymerase Chain Reaction (PCR) is used to replicate segments of DNA. It is used to make DNA samples big enough for testing, starting from very small samples collected, for instance, from a crime scene. PCR can double the number of a particular DNA segment every two minutes. Write an equation for the number of segments as a function of the number of minutes, t, if there is initially just one segment.

Accepted Answer

A)    
B)    
C)    
D)    
A)    
B)    
C)    
D)

Question 17

The differential equation is separable. Find the general solution in an explicit form.

Accepted Answer

A)    
B)    
C)    
D)    
A)    
B)    
C)    
D)

Question 18

Find the solution to the following separable differential equation.   , a is a constant.

Accepted Answer

A)    
B)    
C)    
D)    
A)    
B)    
C)    
D)

Question 19

The number of stores in a particular chain of coffee bars was 100 in 1996 and began growing exponentially with a growth constant of 0.35 year-1. In what year would one predict the number of stores to reach 10,000?

Accepted Answer

A)  1999 
B)  2004 
C)  2009 
D)  2014 
A)  1999 
B)  2004 
C)  2009 
D)  2014

Question 20

Write the following second-order equation as a system of first-order equations.

Accepted Answer

The answer of Write the following second-order equation as a...

Find all equilibrium points for the following coupled predator-prey-model equations.

The differential equation is separable. Find the general solution in an explicit form.

Write the following third-order equation as a system of equations.

Calculate how much you would need to invest now in order to fund a year of college twenty years from now, assuming a year of college costs $26,000 now and is inflating at 6%, and your investment will earn 10%. Assume continuous compounding.

Identify the equilibrium solutions for , and determine if they are stable or unstable.

Use your calculator to construct the direction field for the following differential equation. [Use the standard zoom window.]

Match the appropriate slope field with the differential equation .

Find all equilibrium points for the following coupled equations. Identify each equilibrium point as stable or unstable.

Solve the following initial value problem explicitly.

Use Euler's method with h = 0.1 to approximate y(1.0) and y(2.0) for the differential equation , .

$50,000 that was invested in 1990 was worth $134,100 in 2000. What annual interest rate did the investment earn in that 10 year period? Assume continuous compounding.

In 1995 an investor put $2000 in an account which paid 8%. In 2005 she withdrew $1000 from the account. What will the account be worth in 2020 ?

A particular investment program involves continuously making small investments adding up to $3600 each year. If the investment pays 12%, and the account started off with an initial balance of $500, how much will the account be worth in 40 years?

Find the solution to the following separable differential equation. , a is a constant

The differential equation is separable. Find the general solution in an explicit form.

Find the solution to the following separable differential equation. , a is a constant.

The number of stores in a particular chain of coffee bars was 100 in 1996 and began growing exponentially with a growth constant of 0.35 year^-1. In what year would one predict the number of stores to reach 10,000?

Write the following second-order equation as a system of first-order equations.

Preliminaries

Limits and Continuity

Differentiation

Applications of the Derivative

Integration

Applications of the Definite Integral

Integration Techniques

Infinite Series

Parametric Equations and Polar Coordinates

Vectors and the Geometry of Space

Vector-Valued Functions

Functions of Several Variables and Partial Differentiation

Multiple Integrals

Vector Calculus

Second Order Differential Equations

Filters

Exam 8: First-Order Differential Equations

Find all equilibrium points for the following coupled predator-prey-model equations.

The differential equation is separable. Find the general solution in an explicit form.

Write the following third-order equation as a system of equations.

Calculate how much you would need to invest now in order to fund a year of college twenty years from now, assuming a year of college costs $26,000 now and is inflating at 6%, and your investment will earn 10%. Assume continuous compounding.

Identify the equilibrium solutions for , and determine if they are stable or unstable.

Use your calculator to construct the direction field for the following differential equation. [Use the standard zoom window.]

Match the appropriate slope field with the differential equation .

Find all equilibrium points for the following coupled equations. Identify each equilibrium point as stable or unstable.

Solve the following initial value problem explicitly.

Use Euler's method with h = 0.1 to approximate y(1.0) and y(2.0) for the differential equation , .

$50,000 that was invested in 1990 was worth $134,100 in 2000. What annual interest rate did the investment earn in that 10 year period? Assume continuous compounding.

In 1995 an investor put $2000 in an account which paid 8%. In 2005 she withdrew $1000 from the account. What will the account be worth in 2020 ?

A particular investment program involves continuously making small investments adding up to $3600 each year. If the investment pays 12%, and the account started off with an initial balance of $500, how much will the account be worth in 40 years?

Find the solution to the following separable differential equation. , a is a constant

The differential equation is separable. Find the general solution in an explicit form.

Find the solution to the following separable differential equation. , a is a constant.

The number of stores in a particular chain of coffee bars was 100 in 1996 and began growing exponentially with a growth constant of 0.35 year-1. In what year would one predict the number of stores to reach 10,000?

Write the following second-order equation as a system of first-order equations.

Preliminaries

Limits and Continuity

Differentiation

Applications of the Derivative

Integration

Applications of the Definite Integral

Integration Techniques

Infinite Series

Parametric Equations and Polar Coordinates

Vectors and the Geometry of Space

Vector-Valued Functions

Functions of Several Variables and Partial Differentiation

Multiple Integrals

Vector Calculus

Second Order Differential Equations

Filters

The number of stores in a particular chain of coffee bars was 100 in 1996 and began growing exponentially with a growth constant of 0.35 year^-1. In what year would one predict the number of stores to reach 10,000?