Provide an appropriate response.
-Use the properties of exponents to write the function of the form $f ( t ) = \mathrm { ka } ^ { t }$, where $\mathrm { k }$ is a constant. $f ( t ) = \left( \frac { 1 } { 2 } \right) ^ { 3 - 4 t }$
A) $f ( t ) = 8 \cdot 16 ^ { t }$
B) $f ( t ) = \left( \frac { 1 } { 16 } \right) 8 ^ { t }$
C) $f ( t ) = \left( \frac { 1 } { 8 } \right) 16 ^ { t }$
D) $f ( t ) = \frac { 1 } { 8 } \left( \frac { 1 } { 16 } \right) ^ { t }$

Question

Quizplus · Accepted Answer

The expression $\left( \frac{1}{2} \right)^{3 - 4t}$ can be rewritten using properties of exponents as $\left( \frac{1}{2} \right)^3 \cdot \left( \frac{1}{2} \right)^{-4t}$. This simplifies to $\frac{1}{8} \cdot 16^t$, which matches option C.

Provide an Appropriate Response f(t)=katf ( t ) = \mathrm { ka } ^ { t }f(t)=kat

Provide an Appropriate Response $f ( t ) = \mathrm { ka } ^ { t }$