SOLUTION: Find an exponential function "f" of the form f(x)=b^x that passes through the point (2,1/16).

Algebra ->  Exponential-and-logarithmic-functions -> SOLUTION: Find an exponential function "f" of the form f(x)=b^x that passes through the point (2,1/16).      Log On


   

Question 920255: Find an exponential function "f" of the form f(x)=b^x that passes through the point (2,1/16).
Answer by josgarithmetic(39620) About Me  (Show Source):
You can put this solution on YOUR website!
f=b%5Ex;
Your one and only data point may be insufficient. Base two might be the choice for b.

f=a%2A2%5Ex, including a possible factor of "a".
log%282%2Cf%29=log%282%2Ca%29%2Blog%282%2C2%5Ex%29
log%282%2Cf%29=x%2Alog%282%2C2%29%2Blog%282%2Ca%29
log%282%2C%282%5E-4%29%29=2%2A1%2Blog%282%2Ca%29, when the one data point is substituted.
-4=2%2Blog%282%2Ca%29
highlight_green%28-6=log%282%2Ca%29%29

Convert that into exponential form, and it means 2%5E%28-6%29=a;
highlight_green%28a=1%2F64%29.

highlight%28f%28x%29=%281%2F64%29%282%5Ex%29%29