The value of f(6)=64
Given :
The graph of an exponential function .
Explanation :
We need to find out f(6) using the given graph .
To find f(x), first we find out the function f(x) using the graph .
Pick any two points from the graph (0,1) and (1,2)
General form of exponential function is [tex]y=ab^x[/tex]
Substitute (0,1) in general equation
[tex]1=ab^0\\1=a\\a=1[/tex]
Now we plug in (1,2) in the equation
[tex]y=ab^x\\2=1(b)^1\\2=b\\b=2[/tex]
Substitute a=1, b=2 in [tex]f(x)=ab^x\\[/tex]
[tex]f(x)=1(2)^x\\f(x)=2^x[/tex]
To find out f(6), we plug in 6 for x in f(x)
[tex]f(x)=2^x\\f(6)=2^6\\f(6)=64[/tex]
Learn more : brainly.com/question/3971260
