**Q1: **

Solve the differential equation .

- A
- B
- C
- D
- E

**Q2: **

The logistic population model assumes an upper limit , beyond which growth cannot occur. The population has a rate of change that satisfies for some positive constant . A suitable function involves a second parameter , determined by how rapid the initial growth is. Without integrating, which of the following could be ?

- A
- B
- C
- D
- E

**Q3: **

Solve the differential equation .

- A or
- B or
- C or
- D or
- E or

**Q4: **

Suppose a populationβs growth is governed by the logistic equation , where . Write the formula for .

- A
- B
- C
- D
- E

**Q5: **

Suppose a populationβs growth is governed by the logistic equation , where . Write the formula for .

- A
- B
- C
- D
- E

**Q6: **

Solve the following differential equation by separating it:

- A
- B
- C
- D

**Q7: **

Unlike exponential growth, where a population grows without bound, the logistic model assumes an upper limit , beyond which growth cannot occur. The population has a rate of change that satisfies for some positive constant . Given a population with , at what population is the growth zero?

- A
- B0
- CIt cannot be determined.
- D
- Enever

**Q8: **

Find a 1-parameter family of solutions for the following differential equation:

- A
- B
- CThere is no solution.
- D

**Q9: **

Find the solution of the differential equation given that .

- A
- B
- C
- D

**Q10: **

Find the implicit solution to the following differential equation:

- A
- B
- C
- D

**Q11: **

Which of the following is a solution of defined for all ?

- A
- B
- C
- D

**Q12: **

Find a relation between and given that .

- A
- B
- C
- D
- E

**Q13: **

Find the solution for the following differential equation for :

- A
- B
- C
- D

**Q14: **

Solve the differential equation .

- A
- B
- C
- D

**Q15: **

Suppose a population grows according to a logistic model with an initial population of 1β000 and a carrying capacity of 10β000. If the population grows to 2β500 after one year, what will the population be after another three years?

**Q16: **

Find the solution of the differential equation that satisfies the initial condition .

- A
- B
- C
- D
- E