The exponential function is [tex]f(x)=4^x[/tex]. 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:
[tex]f(x)=ab^x[/tex]
Substituting [tex]x=3, f(x)=64[/tex], we get
[tex]64=ab^3[/tex] ...(i)
Substituting [tex]x=4, f(x)=256[/tex], we get
[tex]256=ab^4[/tex] ...(ii)
Divide equation (ii) by equation (i).
[tex]\dfrac{256}{64}=\dfrac{ab^4}{ab^3}[/tex]
[tex]4=b[/tex]
Substitute [tex]b=4[/tex] in (i).
[tex]64=a(4)^3[/tex]
[tex]64=64a[/tex]
[tex]1=a[/tex]
Substitute [tex]a=1,b=4[/tex] in [tex]f(x)=ab^x[/tex].
[tex]f(x)=(1)(4)^x[/tex]
[tex]f(x)=4^x[/tex]
The exponential function is [tex]f(x)=4^x[/tex]. So, option B is correct.
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