Free Printable Differential equations, Slope Fields, and More!

1.

a)

B

b)

C

c)

D

d)

E

2.

a)

A

b)

C

c)

D

d)

E

3.

a)

A

b)

B

c)

D

d)

E

4.

a)

B

b)

C

c)

D

d)

E

5.

a)

A

b)

B

c)

D

d)

E

6.

a)

A

b)

B

c)

C

d)

D

7.

a)

A

b)

B

c)

C

d)

D

8.

a)

B

b)

C

c)

D

d)

E

9.

Consider the differential equation
dy/dx = e^y(4x²-5x). Let y=f(x) be the particular solution to the differential equation that passes through (1, 0).
Write an equation of the line tangent to the graph of f at the point (1, 0).

a)

y=x-1

b)

y=2(x-1)

c)

y=-(x-1)

d)

y=-2(x-1)

10.

Which of the following equations solves dy/dt = ky?

a)

y = Ce^kt

b)

y = mx + b

c)

y = a(x - h)² + k

d)

y = Asin[B(x - C)] + D

11.

The number of bacteria increases at a rate proportional to the present amount. After 5 hours, there were 80 bacteria and after 8 hours, there were 120 bacteria. How many bacteria were present initially?

a)

1

b)

About 16

c)

About 40

d)

About 53

12.

Greenium has a half-life of 23 years and decays following the Law of Exponential Change. After how many years will 80% of an original amount have decayed?

a)

t = 7.4143 years

b)

t = 10.2646

c)

t = 53.4043 years

d)

t = 74.0341 years

13.

dy/dx = 4x/y. Suppose y(0)=1

The particular solution is

a)

B

b)

C

c)

D

d)

E

14.

a)

A

b)

B

c)

C

d)

D

15.

dy/dx=0.04y(3-y/120). What is the carrying capacity of the population?

a)

0.04

b)

3

c)

120

d)

360

16.

dy/dy=.04y(1-y/100). At what value of y is population increasing the fastest?

a)

100

b)

50

c)

.04

d)

Cannot be determined.

17.

If dy/dt=-2y and if y=1 when t=0, what is the value of t for what y=1/2?

a)

-ln(2)/2

b)

-1/4

c)

ln(2)/2

d)

sqrt(2)/2

e)

ln2

18.

What movie is this picture from?

a)

Little Mermaid

b)

Lady & the Tramp

c)

Bugs Life

d)

Frozen

19.

What movie is this photo from?

a)

Oliver & Company

b)

Lion King

c)

Lady & the Tramp

d)

Jungle Book

20.

who is this

a)

darth vader

b)

darth maul

c)

kylo ren

d)

emperor palpatine

21.

who is this

a)

yoda

b)

jabba

c)

ewok

d)

jawa

22.

who is this

a)

yoda

b)

jabba

c)

ewok

d)

jawa

23.

which ship is this

a)

x-wing

b)

TIE fighter

c)

mellinium falcon

24.

What is the answer to Problem 1?

a)

A

b)

B

c)

C

d)

D

e)

E

25.

A population is modeled by a function P that satisfies the logistic differential equation $\frac{dp}{dt}=2P\left(1-\frac{P}{90}\right),$ where the initial population P(0) = 110 and t is the time in years. For what values of P is the population growing the fastest?

a)

30

b)

45

c)

55

d)

90

26.

Which of the following is not a logistic differential equation?

a)

a

b)

b

c)

c

d)

d

27.

Let g be a function such that

\frac{dy}{dx}=2y\left(3-y\right)

Given that g(4)=1, then

\lim_{x\rightarrow\infty}g\left(x\right)=

(a)

28.

$\frac{dy}{dx}=2y\left(3-x\right)$

True or False: This is a logistic differential equation.

a)

True

b)

False

29.

$P\left(t\right)=\frac{12}{1+Ce^{-0.2t}}$

If P(0)=3, at what value of P is the population growing the fastest?

(a)

30.

What is the moose's name in Frozen?

a)

Sven

b)

Steve

c)

Bud

d)

Jerry

31.

A bacteria culture grows at a constant relative growth rate. The count was 400 after 2 hours and 25,600 after 6 hours. Find the value of k, the constant relative growth rate.

a)

$\frac{\ln\left(64\right)}{4}$

b)

$\frac{\ln\left(64\right)}{6}$

c)

$\frac{e^{64}}{4}$

d)

$\frac{\ln25,600}{4}$

32.

A puppy weighs 2.0 pounds at birth and 3.5 pounds two months later. If the weight of the puppy during its first 6 months is increasing at a rate proportional to its weight, then how much will the puppy weigh when it is 3 months old?

a)

4.2 Pounds

b)

4.6 Pounds

c)

4.8 Pounds

d)

5.6 Pounds

e)

6.5 Pounds

33.

According to Newton’s law of cooling, the rate at which an object cools (or warms) is directly proportional to the temperature difference between the environment and the object itself. If a pot of boiling water (100°C) is left at room temperature (22°C) and after five minutes the water is only 70°C, find its temperature after another 5 minutes.

a)

51°C

b)

52°C

c)

61°C

d)

62°C

e)

63°C

Differential equations, Slope Fields, and More!

Total questions: 33

Worksheet time: 52mins

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