The exponential function is \(f(x)=4^x\). So, option B is correct.
Important information:
- The table of values represents an exponential function.
Exponential function:
The general form of an exponential function is:
\(f(x)=ab^x\)
Substituting \(x=3, f(x)=64\), we get
\(64=ab^3\) ...(i)
Substituting \(x=4, f(x)=256\), we get
\(256=ab^4\) ...(ii)
Divide equation (ii) by equation (i).
\(\dfrac{256}{64}=\dfrac{ab^4}{ab^3}\)
\(4=b\)
Substitute \(b=4\) in (i).
\(64=a(4)^3\)
\(64=64a\)
\(1=a\)
Substitute \(a=1,b=4\) in \(f(x)=ab^x\).
\(f(x)=(1)(4)^x\)
\(f(x)=4^x\)
The exponential function is \(f(x)=4^x\). So, option B is correct.
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