SOLUTION: The equation of curve is y=ax^n. Given that the points (2,9) and (3,4) lie on the curve, calculate the value of a and n. Attempt: 9=a(2)^n n=log2 (9/a) 4=a(3)^n n=log3

Algebra ->  Exponential-and-logarithmic-functions -> SOLUTION: The equation of curve is y=ax^n. Given that the points (2,9) and (3,4) lie on the curve, calculate the value of a and n. Attempt: 9=a(2)^n n=log2 (9/a) 4=a(3)^n n=log3       Log On


   

Question 587956: The equation of curve is y=ax^n. Given that the points (2,9) and (3,4) lie on the curve, calculate the value of a and n.
Attempt:
9=a(2)^n
n=log2 (9/a)
4=a(3)^n
n=log3 (4/a)
Answer by scott8148(6628) About Me  (Show Source):
You can put this solution on YOUR website!
9=a(2)^n ___ log(9) = log(a) + n log(2)

4=a(3)^n ___ log(4) = log(a) + n log(3)

subtracting ___ log(9) - log(4) = n log(2) - n log(3) ___ log(9/4) = n log(2/3)

log[(2/3)^-2] = n log(2/3) ___ -2 log(2/3) = n log(2/3) ___ -2 = n

substituting ___ 9 = a(2^-2) ___ 9 = a(1/4) ___ 36 = a