19-20 Covid Review 2 (Differential Eq, Slope Flds)

The rate of change in area of a region over time is directly proportional the the square of the area. Which of these correctly describes that?

• $\frac{\text{d}A}{\text{d}t}=kA$

• $A\ =\ kA^2$

• $\frac{\text{d}A}{\text{d}t}\ =\ kA^2$

• $A\ =\ kA$

A population P is increasing over time t, measured in years, at a rate that is proportional to the population. Which of these could correctly model that?

•  $\frac{\text{d}P}{\text{d}t}\ =\ -0.34P$  

•  $\frac{\text{d}P}{\text{d}t}\ =\ \frac{-0.11}{P}$  

•  $\frac{\text{d}P}{\text{d}t}\ =\ 0.032P$  

•  $\frac{\text{d}P}{\text{d}t}\ =\ \frac{0.12}{P}$  

The rate of change in y with respect to x is inversely proportional to the square root of x. Which of these models that?

•  $\frac{\text{d}x}{\text{d}y}\ =\ \frac{k}{x^2}$  

•  $\frac{\text{d}x}{\text{d}y}\ =\ \frac{k}{\sqrt{x}}$  

•  $\frac{\text{d}x}{\text{d}y}\ =\ kx^2$  

•  $\frac{\text{d}x}{\text{d}y}\ =\ kx^2$  

There are S students at a school. The rate at which the number of students who have tried a new app A is growing at a rate that is jointly proportional to the number of students who have tried the app to those who have not tried it.

• $\frac{\text{d}A}{\text{d}t}\ =\ k\times S\times A$

• $\frac{\text{d}A}{\text{d}t}\ =\ k\times\frac{S}{A}$

• $\frac{\text{d}A}{\text{d}t}\ =\ k\times A$

• $\frac{\text{d}A}{\text{d}t}\ =\ k\times A\left(S-A\right)$

Of the following, which is a solution to the differential equation, select all that apply:
 $y''-6y'+8y=0$  

•  $y=2\sin\left(4x\right)$  

•  $y=3e^{2x}$  

•  $y=Ce^{4x},\$  where C is a constant

The function  $y\ =\ 4\sin\left(2x\right)\ -\ 3\cos\left(4x\right)$  satisfies which of these differential equations?

•  $y''\ +\ 4y\ =\ 36\cos\left(4x\right)$  

•  $y''\ +\ 4y\ =\ 0$  

•  $y''-4y=36\cos\left(4x\right)$  

•  $y''-4y=0$  

For what value of k, if any, will  $y=ke^{-2x}+4\cos\left(3x\right)$  be a solution to the differential equation  $y''\ +\ 9y\ =\ 26e^{-2x}$  ?

• 2

• 13/5

• 26

• No value of k

Which slope field is represented by dy/dx = x²?

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• 
• 
• 

Tags

CCSS.HSA.CED.A.2

CCSS.HSA.REI.D.10

Which choice below represents this slope field?

• dy/dx = 2x

• dy/dx = -2x

• dy/dx = x

• dy/dx = x²

Which equation below represents the slope field?

• dy/dx = x - 2

• dy/dx = 1/2x + 1

• dy/dx =1/2 y - 2

• dy/dx = y + 2

Tags

CCSS.HSA.CED.A.2

CCSS.HSA.REI.D.10