Answer:
197
Step-by-step explanation:
Initial population of rabbit is 139
after 2 years , rabbit population is 556
For exponential growth use y=ab^x
where a is the initial population
x is the time period
b is the growth rate, y is the final population
a= 139 is already given
when x=2, the value of y = 557
plug in all the values in the formula and find out 'b'
[tex]y=ab^x[/tex]
[tex]557=139(b)^2[/tex]
Divide both sides by 139
[tex]\frac{557}{139} =b^2[/tex]
take square root on both sides
b=2.00180 and b=-2.00180
growth factor cannot be negative
So b= 2.0018
The equation y=ab^x becomes
[tex]y=139(2.0018)^x[/tex]
To find population after 6 months
1 year = 12 months
so 6 months = 0.5 years
we plug in 0.5 for x
[tex]y=139(2.0018)^{0.5}[/tex]
y= 196.66
so population after 6 months = 197
