Question

1- Assume a pond’s carrying capacity of frogs is 300 and the intrinsic growth rate is 0.3. What is the growth rate of frogs if there are 30 individuals currently present? Hint: dN/dt=rN((K-N)/K).

a. 8

b. 5

c. 13

d. 3

2- If a starting population of cicadas is 100, the birth rate per capita is 0.6, the death rate per capita is 0.3, how big will the population of cicadas at 10 years? Hint: Nt=N0ert, r=b-d, and e=2.718.

a. about 500

b. about 2000

c. about 1000

d. about 3000

3- A flask containing Paramecium currently has 300 individuals. If the carrying capacity of the flask is 3000 individuals and the rmax is 0.3, what is the intrinsic growth rate? Hint: r=rmax((K-N)/K).

a. 0.69

b. 0.30

c. 0.03

d. 0.27

4- If the rate of deer population growth is -0.00001, and the population is 3000, what is the carrying capacity of the deer population?

a. Probably 3000 as the growth rate is decreasing, but not by a lot.

b. Probably 2000 because it's not hunting season.

c. Probably 5000 as the growth rate is decreasing.

d. Probably 2000 as the growth rate is decreasing, meaning the carrying capacity has been overshot.

5- If a population of mice started with 300 individuals and grew to 600 in 1.5 years, what is the intrinsic rate of population increase (r)? Hint: N=ln2/r.

a. 0.92

b. 0.23

c. 0.12

d. 0.46

Answer 1

1. Carrying capacity=K =300

Number of individuals =N=30

Intrinsic growth rate=r=0.3

Growth rate= dN/dT =rN((K-N)/K)

=0.3*30*((300-30)/300)=9*270/300 =8.1=8 OPTION a is correct.

2. Starting Population = N0 =100

Birth rate per capita =b=0.6

Death rate per capita = d= 0.3

Intrinsic growth rate =r=b-d=0.6-0.3=0.3

euler's number= e=2.718

t= 10 years

Population after 10 years = N=NOert =100*2.718(0.3*10) =100*2.7183 = 100*20.079=2007.9

Therefore, the population will be around 2000.Option b.is correct

3. r max = maximum population growth rate = 0.3

Carrying capacity K= 3000

Present population =300

Intrinsic growth rate =r=rmax((K-N)/K) = 0.3 *((3000-300/3000) = 0.3*2700/3000= 0.27

Option d. is correct.

4.Option d is correct. Carrying capacty should be around 2000 as the groth rate is decreasing and the opulation has shot above the carrying capacity leading to lack of resouces, food etc. due to which the deer population is dwindiling.

5.The population doubled from 300 to 600 in 1.5 years.

t double =ln 2/r =1.5

Intrinsic rate of population increase= r=ln2/t double =0.69/1.5=0.46 option d.is correct