Question

A population of snails is located in a lake that has a carrying capacity of 20,000 snails. The intrinsic capacity for increase for these snails is 0.15 and the current population is 12,000. In a year, how big do you expect the snail population to be?

A. 13,800
B. 20,000
C. 12,720
D. 16,840

Answer 1

Answer: C. 12,720

Explanation:

In Logistic growth, the change in population is given by :

`(dP)/(dt)=rP\left(1-(P)/(C)\right)` ...(*)

, where P= Initial population , t= time , r= intrinsic rate and
`(dP)/(dt)`=Change in population and C = Carrying capacity.

As per given , we have

P=12,000

r=0.15

C=20,000

t=1 year

Substitute all values in (*) , we get

`(dP)/(dt)=(0.15)(12000)\left(1-(12000)/(20000)\right)\\\\=(1800)(0.4)\\=720`

Now, Total population of snails after a year =
`P+(dP)/(dt)=12,000+720=12,720`

Hence, the correct answer is C. 12,720 .