Question

which equation represents an exponential function that passes through the point (2, 36)?

• ( f(x) = 4(3)^x )
• ( f(x) = 4(x)^3 )
• ( f(x) = 6(3)^x )
• ( f(x) = 6(x)^3 )

Explanation:

Step1: Recall exponential function form

An exponential function has the form $f(x)=a(b)^x$ (not $a(x)^b$, which is polynomial). So eliminate options with $x$ as the base: $f(x)=4(x)^3$ and $f(x)=6(x)^3$.

Step2: Test remaining option 1

Substitute $x=2$ into $f(x)=4(3)^x$:
$f(2)=4(3)^2=4\times9=36$

Step3: Verify it matches the point

The result equals the y-value of the given point $(2,36)$.

Step4: Test remaining option 3 (confirmation)

Substitute $x=2$ into $f(x)=6(3)^x$:
$f(2)=6(3)^2=6\times9=54
eq36$

Answer:

A. $f(x)=4(3)^x$