Question 1

Twenty-five rabbits were brought to a zoo 15 years ago.
At present there are 35 rabbits in the zoo. The zoo can support a maximum of 180 rabbits.
Assuming a logistic growth model, when will the rabbit population reach 50, 100, and 180 rabbits?

Accepted Answer

The answer of Twenty-five rabbits were brought to a zoo...

Question 2

A rat population in a certain field is initially 500. After 3 years, the population increases to 700. Assuming logistic growth with a carrying capacity of 1000, how long after reaching 700 will it take for the population to reach 800?

Accepted Answer

The answer of A rat population in a certain field...

Question 3

A deer population for a certain area is initially  . After 6 years, the population increases to 250. After another 4 years, the population increases to 300. Assuming logistic growth with a carrying capacity of 400, what is  ?

Accepted Answer

The answer of A deer population for a certain area...

Question 4

Solve the initial value problem  .

Accepted Answer

The answer of Solve the initial value problem  ....

Question 5

The differential equation  is:
A) linear.
B) nonlinear, but it becomes linear if  is the independent variable.
C) separable.
D) nonseparable, but it becomes separable if  is the independent variable.
E) none of the above.

Accepted Answer

The answer of The differential equation  is:
A) linear.
B) nonlinear,...

Question 6

A deer population for a certain area was 400 at the beginning of the year 1995. After 2 years, the population increased to 500. Assuming logistic growth with a carrying capacity of 800, express the population as a function of t, the number of years since the beginning of 1995.

Accepted Answer

The answer of A deer population for a certain area...

Question 7

A deer population for a certain area is initially 350. After 2 years, the population increases to 650. Assuming logistic growth with a carrying capacity of 1200, how long after reaching 650 will it take the population to reach 1000?

Accepted Answer

The answer of A deer population for a certain area...

Question 8

A deer population for a certain area is initially 500. After 3 years, the population increases to 600. Assuming logistic growth with a carrying capacity of 850, what is the deer population 2 years after the population reached 600?

Accepted Answer

The answer of A deer population for a certain area...

Question 9

Thirty birds were brought to a zoo 10 years ago.
At present, there are 60 birds in the zoo. The zoo can support a maximum of 120 birds.
Assuming a logistic growth model, when will the bird population reach 80, 100, and 120 birds?

Accepted Answer

The answer of Thirty birds were brought to a zoo...

Question 10

Solve the linear equations.
A)  
B)  (Hint: rewrite for  .)

Accepted Answer

The answer of Solve the linear equations.
A)  
B) ...

Question 11

Twenty panda bears were brought to a national park 20 years ago. At present, there are 42 bears in the park. The park can support a maximum of 200 bears. Assuming a logistic growth model, when will the bear population reach 80, 150, and 200 bears?

Accepted Answer

The answer of Twenty panda bears were brought to a...

Question 12

Let  be a population of insects that is modeled by the logistic equation:  
A) Determine the equilibrium solutions and their stabilities.
B) What is the long term behavior of the population?
C) Find the value of  at the inflection point and explain its meaning referring to the population growth. 
D) Solve the logistic equation and verify your answer to B.

Accepted Answer

The answer of Let  be a population of insects...

Question 13

Let  be the population of a certain animal species, satisfying the logistic equation  
A) Determine the equilibrium solutions and their stabilities.
B) What is the long term behavior of the population?
C) Find the value of  at the inflection point and explain its meaning referring to the population growth. 
D) Solve the logistic equation and verify your answer to B.

Accepted Answer

The answer of Let  be the population of a...

Question 14

Solve the following differential equations.
A)  
B)  (Hint: rewrite for  .)

Accepted Answer

The answer of Solve the following differential equations.
A)  
B)...

Question 15

A rat population for a certain field is 300 at the beginning of the year 2002.. After 4 years, the population increased to 700. Assuming logistic growth with a carrying capacity of 900, express the population as a function of t, the number of years since the beginning of 2002.

Accepted Answer

The answer of A rat population for a certain field...

Question 16

A rat population for a certain field is initially  . After 3 years, the population increases to 450. After another 2 years, the population increases to 650. Assuming logistic growth with a carrying capacity of 900, what is  ?

Accepted Answer

The answer of A rat population for a certain field...

Question 17

A rat population in a certain field is initially 200. After 4 years, the population increases to 350. Assuming logistic growth with a carrying capacity of 550, what is the rat population 3 years after the population reached 350?

Accepted Answer

The answer of A rat population in a certain field...

Question 18

Bees in a certain region are born at a rate that is proportional to their current population. Without any outside factors the population doubles in 3 weeks' time. It was observed that each day 12 bees joined the population, 10 were caught by men, and 5 died of natural causes.
Determine whether the population will survive if initially it counted 100 bees. If not, when will it die out?

Accepted Answer

The answer of Bees in a certain region are born...

Question 19

A 1200-gallon tank initially contains 500 gallons of water with 4 lbs of salt dissolved in it. Water with a salt concentration of 2 lbs/gal enters the tank at a rate of 10 gal/h, while the solution leaves the tank at a rate of 6 gal/h. Find the amount of salt in the tank when it overflows.

Accepted Answer

The answer of A 1200-gallon tank initially contains 500 gallons...

Question 20

Solving the differential equation  , we obtain the solution:
A)  .
B)  .
C)  .
D)  .
E)  .

Accepted Answer

The answer of Solving the differential equation  , we...

Quiz 10: Introduction to Differential Equations

Twenty-five rabbits were brought to a zoo 15 years ago. At present there are 35 rabbits in the zoo. The zoo can support a maximum of 180 rabbits. Assuming a logistic growth model, when will the rabbit population reach 50, 100, and 180 rabbits?

A rat population in a certain field is initially 500. After 3 years, the population increases to 700. Assuming logistic growth with a carrying capacity of 1000, how long after reaching 700 will it take for the population to reach 800?

A deer population for a certain area is initially . After 6 years, the population increases to 250. After another 4 years, the population increases to 300. Assuming logistic growth with a carrying capacity of 400, what is ?

Solve the initial value problem .

The differential equation is:

A deer population for a certain area was 400 at the beginning of the year 1995. After 2 years, the population increased to 500. Assuming logistic growth with a carrying capacity of 800, express the population as a function of t, the number of years since the beginning of 1995.

A deer population for a certain area is initially 350. After 2 years, the population increases to 650. Assuming logistic growth with a carrying capacity of 1200, how long after reaching 650 will it take the population to reach 1000?

A deer population for a certain area is initially 500. After 3 years, the population increases to 600. Assuming logistic growth with a carrying capacity of 850, what is the deer population 2 years after the population reached 600?

Thirty birds were brought to a zoo 10 years ago. At present, there are 60 birds in the zoo. The zoo can support a maximum of 120 birds. Assuming a logistic growth model, when will the bird population reach 80, 100, and 120 birds?

Solve the linear equations. A) B) (Hint: rewrite for .)

Twenty panda bears were brought to a national park 20 years ago. At present, there are 42 bears in the park. The park can support a maximum of 200 bears. Assuming a logistic growth model, when will the bear population reach 80, 150, and 200 bears?

Solve the following differential equations. A) B) (Hint: rewrite for .)

A rat population for a certain field is 300 at the beginning of the year 2002.. After 4 years, the population increased to 700. Assuming logistic growth with a carrying capacity of 900, express the population as a function of t, the number of years since the beginning of 2002.

A rat population for a certain field is initially . After 3 years, the population increases to 450. After another 2 years, the population increases to 650. Assuming logistic growth with a carrying capacity of 900, what is ?

A rat population in a certain field is initially 200. After 4 years, the population increases to 350. Assuming logistic growth with a carrying capacity of 550, what is the rat population 3 years after the population reached 350?

A 1200-gallon tank initially contains 500 gallons of water with 4 lbs of salt dissolved in it. Water with a salt concentration of 2 lbs/gal enters the tank at a rate of 10 gal/h, while the solution leaves the tank at a rate of 6 gal/h. Find the amount of salt in the tank when it overflows.

Solving the differential equation , we obtain the solution: