Deck 6: Section 4: Differential Equations

Question 1

Each of the following graphs is from a logistic function . Which one has the largest value of b?

A)
B)
C)
D)
E)

Answer 1

Question 2

Identify the graph of the logistic function .

A)
B)
C)
D)
E)

Answer 2

Question 3

A conservation organization releases 30 panthers into a preserve. After 3 years, there are 50 panthers in the preserve. The preserve has a carrying capacity of 150. Determine the time it takes for the population to reach 110.

A) 13.139 years
B) 8.994 years
C) 10.378 years
D) 7.811 years
E) 12.003 years

Answer 3

10.378 years

Question 4

A conservation organization releases 50 foxes into a preserve. After 5 years, there are 85 foxes in the preserve. The preserve has a carrying capacity of 225. Determine the population after 10 years. Discard any fractional part of your answer.

A) 126
B) 118
C) 139
D) 131
E) 205

Question 5

A conservation organization releases 40 coyotes into a preserve. After 4 years, there are 70 coyotes in the preserve. The preserve has a carrying capacity of 175. Write a logistic function that models the population of coyotes in the preserve.

A)
B)
C)
D)
E)

Question 6

The logistic function models the growth of a population. Identify the initial population.

A) 6
B) 8
C) 3
D) 24
E) 2

Question 7

The logistic function models the growth of a population. Identify the value of k.

A) 1.7
B) 2.2
C) 0.2
D) 20
E) 0.5

Question 8

Each of the following graphs is from a logistic function . Which one has the smallest value of b?

A)
B)
C)
D)
E)

Question 9

Match the logistic differential equation and initial condition with the graph of its solution shown below.

A)
B)
C)
D)
E)

Question 10

The logistic function models the growth of a population. Identify the maximum carrying capacity.

A) 20
B) 1.7
C) 0.5
D) 0.2
E) 2.2

Question 11

Find the logistic equation that satisfies the following differential equation and initial condition.

A)
B)
C)
D)
E) none of the above

Question 12

The logistic function models the growth of a population. Determine when the population reaches one-half of the maximum carrying capacity. Round your answer to three decimal places.

A) 0.549
B) 3.333
C) 1.151
D) 5.000
E) 1.000

Question 13

The logistic function models the growth of a population. Determine when the population reaches of the maximum carrying capacity. Round your answer to three decimal places.

A) 4.317
B) 3.000
C) 0.474
D) 0.677
E) 0.301

Question 14

Match the logistic equation and initial condition with the graph of the solution.

A)
B)
C)
D)
E)