Use a graphing calculator to estimate the solution set of the equation. Round to the nearest hundredth.
-$$\left( \frac { 1 } { 2 } \right) ^ { x } = 18$$
A) $\{ - 0.24 \}$
B) $\{ - 9.00 \}$
C) $\{ - 4.17 \}$
D) $\{ 4.17 \}$

Question

Quizplus · Accepted Answer

To solve the equation $\left( \frac { 1 } { 2 } \right) ^ { x } = 18$, you can use a graphing calculator to graph the function $y = \left( \frac { 1 } { 2 } \right) ^ { x }$ and find the x-value where $y = 18$. Since $\left( \frac { 1 } { 2 } \right) ^ { x }$ decreases as $x$ increases and $18$ is a relatively large number given the base of the exponent is less than $1$, the solution will be a negative number. Among the options, $\{ - 4.17 \}$ is the only negative value that makes sense in this context, indicating it is the correct estimate for the solution.

Use a Graphing Calculator to Estimate the Solution Set of the Equation