SOLUTION: If the graph of {{{f(x)=b^x}}} asses through the point (2,9), find f(4)

Algebra ->  Exponential-and-logarithmic-functions -> SOLUTION: If the graph of {{{f(x)=b^x}}} asses through the point (2,9), find f(4)      Log On


   

Question 130631: If the graph of f%28x%29=b%5Ex asses through the point (2,9), find f(4)
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
Since the graph passes through the point (2,9), this means that when x=2, then y=9.

y=b%5Ex Start with the given equation


9=b%5E2 Plug in x=2 and y=9. Notice how the only unknown left is b


sqrt%289%29=sqrt%28b%5E2%29 Take the square root of both sides to isolate b


sqrt%289%29=b Take the square root of b%5E2 to get b


b=3 Take the square root of 9 to get 3


So our equation becomes


y=3%5Ex


Now to evaluate f(4), simply plug in x=4

y=3%5E4 Plug in x=4


y=81 Evaluate 3 to the fourth power to get 81


Since "y" is equivalent to f(x), this means that f%284%29=81