SOLUTION: find the equation of an exponential function y=b^x that passes through the point (2,1/4) I plug in the values to the equation 4 = b^2, then change them to natural logs, ln 1/

Algebra ->  Exponential-and-logarithmic-functions -> SOLUTION: find the equation of an exponential function y=b^x that passes through the point (2,1/4) I plug in the values to the equation 4 = b^2, then change them to natural logs, ln 1/      Log On


   

Question 784644: find the equation of an exponential function y=b^x that passes through the point (2,1/4)
I plug in the values to the equation 4 = b^2, then change them to natural logs,
ln 1/4 = 2 ln b
am I on the right track?
Found 2 solutions by josgarithmetic, edjones:
Answer by josgarithmetic(39620) About Me  (Show Source):
You can put this solution on YOUR website!
y=b%5Ex would have some general ordered pairs of points, (x,y) same as (x,b^x). If given the specific point, (2, 1/4), then fit this into the equation form as 1%2F4=b%5E2. What is b?

1%2F4=%281%2F2%29%5E2,
b%5E2=%281%2F2%29%5E2
The simpler answer is highlight%28b=1%2F2%29

To finish, x might be any real number, which is why it seems best to choose the positive form of b.
highlight%28y=%281%2F2%29%5Ex%29

Answer by edjones(8007) About Me  (Show Source):
You can put this solution on YOUR website!
y=b^x (2,1/4)
x=2, y=1/4
b^2=1/4
b=+-(1/2)
.
Ed