Given a power function of the form f(x)=axn, with f(3)=20 and f(9)=1620, find n and a
Correction: f(x)=ax^n
sub in the points
20 = a(3)^n (#1)
1620 = a(9)^n or
1620 = a(3)^(2n) (#2)
divide equation #2 by #1
81 = 3^n
n = 4
sub back into #1
20 = a(3)^4
a = 20/81
a=20/81 , n=4 , f(x) = (20/81)x^4
F (x) = 9-ax
To find the values of n and a in the power function f(x) = ax^n, we can use the given information f(3) = 20 and f(9) = 1620.
Step 1: Start with the equation f(x) = ax^n.
Step 2: Substitute x = 3 into the equation to get f(3) = a(3)^n = 20.
Step 3: Substitute x = 9 into the equation to get f(9) = a(9)^n = 1620.
Now, we have two equations:
a(3)^n = 20 ----- (Equation 1)
a(9)^n = 1620 ----- (Equation 2)
Divide Equation 2 by Equation 1:
[a(9)^n] / [a(3)^n] = 1620 / 20
(9/3)^n = 81
3^n = 81
Since 3^n = 81, we can see that n = 4, since 3^4 = 81.
Now, substitute n = 4 into Equation 1:
a(3)^4 = 20
81a = 20
a = 20/81
So, n = 4 and a = 20/81.