The 470 squirrels will be in 3 years, if a population of 280 flying squirrels in a town in Honduras is growing at a rate of 9% every 6 months.
Step-by-step explanation:
The given is,
280 flying squirrels
Growing at a rate of 9% every 6 months
Step:1
Formula to calculate the squirrels,
[tex]y = A (1+r)^{t}[/tex]...........................(1)
where, A = Initial count
r = Growing rate
t = Time
From the given,
A = 280 squirrels
r = 9 % = 0.09
t = 6 ( Growing rate is given for 6 months, for 3 years 36 months available, so t =[tex]\frac{36}{6}[/tex] = 6)
From equation (1),
[tex]y =280(1+0.09)^{6}[/tex]
[tex]= 280 (1.09)^{6}[/tex]
= (280)(1.6771)
= 469.588
Squirrels after 3 years, y ≅ 470 squirrels
( or )
Step:1
Year will be converted to months,
3 years = 36 months
For 6 months,
[tex]=( Squirrels count )( Rate of grow ) +Squirrels count[/tex]
= (280 × 0.09)+280 = 305.2 squirrels
For 12 months,
[tex]=( Squirrels count )( Rate of grow ) +Squirrels count[/tex]
= (305.2 × 0.09)+305.2 = 332.668 squirrels
For 18 months,
[tex]=( Squirrels count )( Rate of grow ) +Squirrels count[/tex]
= (332.668 × 0.09)+332.668 = 362.608 squirrels
For 24 months,
[tex]=( Squirrels count )( Rate of grow ) +Squirrels count[/tex]
= (362.608 × 0.09)+362.608 = 395.243 squirrels
For 30 months,
[tex]=( Squirrels count )( Rate of grow ) +Squirrels count[/tex]
= (395.243 × 0.09)+395.243 = 430.815 squirrels
For 36 months,
[tex]=( Squirrels count )( Rate of grow ) +Squirrels count[/tex]
= (430.815 × 0.09)+430.815 = 469.588 squirrels
Squirrels after 3 years, y ≅ 470 squirrels
Result:
The 470 squirrels will be in 3 years, if a population of 280 flying squirrels in a town in Honduras is growing at a rate of 9% every 6 months.
