SOLUTION: Write a power function y=ax^b whose graph passes through the given points: A) (2,2)(4,16) B.) (3,3),(6,12)

Algebra ->  Exponential-and-logarithmic-functions -> SOLUTION: Write a power function y=ax^b whose graph passes through the given points: A) (2,2)(4,16) B.) (3,3),(6,12)      Log On


   

Question 144344: Write a power function y=ax^b whose graph passes through the given points: A) (2,2)(4,16) B.) (3,3),(6,12)
Answer by scott8148(6628) About Me  (Show Source):
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A. substituting __ 2=a2^b

substituting __ 16=a4^b

dividing __ 16/2=(a4^b)/(a2^b) __ 8=(4^b)/(2^b) __ 8=(4/2)^b __ 8=2^b

__ taking logarithm __ log(8)=b(log(2)) __ log(8)/log(2)=b __ 3=b

substituting __ 2=a(2^3) __ 2=8a __ 1/4=a


B. substituting __ 3=a3^b

substituting __ 12=a6^b

dividing __ 12/3=(a6^b)/(a3^b) __ 4=(6^b)/(3^b) __ 4=(6/3)^b __ 4=2^b

__ taking logarithm __ log(4)=b(log(2)) __ log(4)/log(2)=b __ 2=b

substituting __ 3=a(3^2) __ 3=9a __ 1/3=a