Unit 8 Test Review - Differential Equations

Which differential equation is represented by the slope field?

• dy/dx = -y

• dy/dx = 1

• dy/dx = -1

• dy/dx = -x

Which slope field below is dy/dx = -x/y

• 
• 
• 
• 

Which function would make this slope field?

• y = 8

• y = x

• y = x²

• y = 2x

A puppy gains weight, w, at a rate approximately inversely proportional to its age, t, in months.

• A

• B

• C

• D

Tags

CCSS.HSF.LE.A.2

dy/dx = 4x/y.  Suppose y(0)=1
The particular solution is

• B
• C
• D
• E

Water flows continuously from a large tank at a rate proportional to the amount of water in the tank, modeled by dy/dt = ky.  There was initially 10,000 ft^3 at t=0.  After 4 hours there were 8000 ft^3 remaining.
What is the value of k in the differential equation (calculator)

• -0.050
• -0.056
• -.169
• -.200

Y is proportional to the difference of x and z

• y= x-z

• y= k(z-x)

• y= k(x-z)

• y= z-x

Tags

CCSS.6.EE.C.9

y is proportional to the product of z and the square root of x

Find the mistake if possible:

• The Diff EQ is solved correctly

• Step 1 is incorrect. The separation of variables wasn't done correctly.

• Step 2 is incorrect. They didn't integrate x² correctly.

• Step 3 is incorrect. They didn't take the reciprocal of x³/3+C correctly.

During a certain epidemic, the number of people that are infected at any time increases at a rate proportional to the number of people that are infected at that time. If 1,000 people are infected when the epidemic is first discovered, and 1,200 are infected 7 days later, how many people are infected 12 days after the epidemic is first discovered?

• 343

• 1343

• 1367

• 1400

• 2057