Provide an appropriate response.
-Give an equation of the form $f ( x ) = a ^ { x }$ to define the exponential function whose graph contains the point $\left( 2 , \frac { 1 } { 49 } \right)$. Assume that $a 0$.
A) $f ( x ) = 2 ^ { x }$
B) $f ( x ) = \left( \frac { 1 } { 7 } \right) ^ { x }$
C) $f ( x ) = 7^ x$
D) $f ( x ) = \left( \frac { 1 } { 2 } \right) ^ { x }$

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 $\left( 2 , \frac { 1 } { 49 } \right)$. Assume that $a > 0$.
A) $f ( x ) = 2 ^ { x }$
B) $f ( x ) = \left( \frac { 1 } { 7 } \right) ^ { x }$
C) $f ( x ) = 7^ x$
D) $f ( x ) = \left( \frac { 1 } { 2 } \right) ^ { x }$

Quizplus · Accepted Answer

Given the point $(2, \frac{1}{49})$, substituting into $f(x) = a^x$ gives $a^2 = \frac{1}{49}$. Solving for $a$ yields $a = \frac{1}{7}$, so the correct equation is $f(x) = \left(\frac{1}{7}\right)^x$.

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

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