Answer: C. 12,720
Step-by-step explanation:
In Logistic growth, the change in population is given by :
[tex]\dfrac{dP}{dt}=rP\left(1-\dfrac{P}{C}\right)[/tex] ...(*)
, where P= Initial population , t= time , r= intrinsic rate and [tex]\dfrac{dP}{dt}[/tex]=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
[tex]\dfrac{dP}{dt}=(0.15)(12000)\left(1-\dfrac{12000}{20000}\right)\\\\=(1800)(0.4)\\=720[/tex]
Now, Total population of snails after a year = [tex]P+\dfrac{dP}{dt}=12,000+720=12,720[/tex]
Hence, the correct answer is C. 12,720 .
