Slope Fields
Growth/Decay
Separation of Var.
Derivatives
Timed Unit Circle
100
Is this a slope field for a differential equation with x, a differential equation with y, or a differential equation with x & y? 
differential equation with x
100
The rate of change of N with respect to t is proportional to (500 - t). Write this as a mathematical equation.
(dN)/dt = k(500 - t)
100
Separate the variables for the differential equation.
dy/dx = 5xy
dy/y = 5xdx
100
State the derivative of
sec(x)
sec(x)tan(x)
100
Find the exact value of
cos(pi/6)
sqrt(3)/2
200
Is this a differential equation with x, a differential equation with y, or a differential equation with x & y? 
a differential equation with x & y
200
Population y grows according to the equation dy/dt = ky, where k is a constant and t is measured in years. If the population doubles every 15 years, what is the value of k? Give an exact answer.
k = ln(2/15)
200
Find the general solution for y:
dy/dx = (x + 1)/y
y=+-sqrt(x^2+2x+C
200
State the derivative of
csc(3x)
-3csc(3x)cot(3x)
200
Find the exact value of
tan((3pi)/2)
Undefined
300
For the slope field pictured, when is dy/dx undefined? Answer in the form of an equation.
y = 0
300
A baby weighs 6 lbs at birth and 9 lbs 3 months later. If the weight of the baby is increasing at a rate proportional to its weight. Find the value of k. Give answer as an exact value.
k = ln(1.5)/3
300
Solve the initial value problem explicitly.
dy/dx = -x/y
(3, 4)
y = sqrt(-x^2+25)
300
State the derivative of ln(x2) in simplified form with positive exponents.
2/x
300
Find the exact value of
csc(pi/3)
(2sqrt(3))/3
400
When does the slope field have a slope of -1? Answer in the form of an equation.
y=-x-1
400
Bacteria in a certain culture increases at a rate proportional to the number present. If the number of bacteria doubles every four hours, in how many hours will the number of bacteria triple? Round to 2 decimal places.
t = 6.34
400
Solve the initial value problem explicity.
dy/dx =sin(5x + pi);
y = 2 when x = 0.
y = -1/5cos(5x + pi) + 9/5
400
Calculate the derivative of y = 5(x2+17)2. Give anwer in simplified form.
y' = 20x3 + 340x
400
Find the exact value of
sec((-3pi)/4)
-sqrt(2)
500
The slope field for a differential equation is shown. Which statement(s) is/are true for solutions of the differential equation?
I. For x < 0, all solutions are decreasing.
II. All solutions level off near the x-axis.
III. For y > 0, all solutions are increasing.
II and III only
500
Newton's Law of Cooling states that the rate of change in the temperature of an object is proportional to the difference between the object's temperature and the temperature in the surrounding area. A detective finds a murder victim at 9 am with a body temp of 90.3 degrees. 1-hour later, the temperature of the body is 89 degrees. The room is kept at 68 degrees (eq: dT/dt = k(T - 68)) Assuming the body was 98.6 degrees at time of death, at what time did the murder occur? Approximate to the nearest 1/4 hour.
3:45 am
500
Solve the initial value problem explicitly.
dy/dx =y/(9 + x)
for (0, 18)
y = 2x + 18
500
Find dy/dx if
3xy = 4x + y^2
(4 - 3y)/(3x - 2y)
500
sin((2pi)/3)-cos((2pi)/3)
Give the exact value of the expression above as a single fraction.
(sqrt(3) + 1)/2