Answer:
5(1.05)^(9x+1)
Step-by-step explanation:
G(x) * B(x)
5(1.05)^(x+1) * (1.05)^8x
rules of exponents: Product Rule: am ∙ an = am + n
so,
5(1.05)^(9x+1)
Answer:
Total No of Butter flies in region is [tex]5(1.05)^{9x+1}[/tex].
Step-by-step explanation:
No of Butterfly gardens in a region after x years , G(x) = [tex]5(1.05)^{x+1}[/tex]
No of Butterflies in a garden after x years , B(x) = [tex](1.05)^{8x}[/tex]
Total No of Butter flies in region , T(x) = G(x) × B(x)
T(x) = [tex]5(1.05)^{x+1}\times(1.05)^{8x}[/tex]
= [tex]5(1.05)^{(x+1)+8x}[/tex] (using law of exponent: [tex]x^a\times x^b=x^{a+b}[/tex])
= [tex]5(1.05)^{9x+1}[/tex]
Therefore, Total No of Butter flies in region is [tex]5(1.05)^{9x+1}[/tex].
