Provide an appropriate response.
-Give an equation of the form $f ( x ) = a ^ { x }$ to define the exponential function whose graph contains the point $\left( 4 , \frac { 1 } { 1296 } \right)$. Assume that $\mathrm { a } 0$.
A) $f ( x ) = 6 ^ { x }$
B) $f ( x ) = \left( \frac { 1 } { 4 } \right) ^ { x }$
C) $f ( x ) = 4 ^ { x }$
D) $f ( x ) = \left( \frac { 1 } { 6 } \right) ^ { x }$

Question

Provide an appropriate response.
-Give an equation of the form $f ( x ) = a ^ { x }$ to define the exponential function whose graph contains the point $\left( 4 , \frac { 1 } { 1296 } \right)$. Assume that $\mathrm { a } > 0$.
A) $f ( x ) = 6 ^ { x }$
B) $f ( x ) = \left( \frac { 1 } { 4 } \right) ^ { x }$
C) $f ( x ) = 4 ^ { x }$
D) $f ( x ) = \left( \frac { 1 } { 6 } \right) ^ { x }$

Quizplus · Accepted Answer

To find the correct equation, we substitute the given point $(4, \frac{1}{1296})$ into the general form $f(x) = a^x$ and solve for $a$. Substituting gives $\frac{1}{1296} = a^4$. The number 1296 is $6^4$, so $a^4 = \left(\frac{1}{6}\right)^4$, which means $a = \frac{1}{6}$. Therefore, the correct equation is $f(x) = \left(\frac{1}{6}\right)^x$.

Provide an Appropriate Response f(x)=axf ( x ) = a ^ { x }f(x)=ax

Provide an Appropriate Response $f ( x ) = a ^ { x }$