Solve the following graphically. If necessary, round answers to the nearest thousandth.
-$$500 ( 1 - 0.03 ) ^ { 2 x } = 250$$
A) $\{ - 46.900 \}$
B) $\{ - 192.652 \}$
C) $\{ 11.378 \}$
D) $\{ 45.5131461 \}$

Question

Quizplus · Accepted Answer

To solve the equation graphically, we first simplify it to find the value of $x$. The equation is $500(1 - 0.03)^{2x} = 250$. Dividing both sides by 500, we get $(1 - 0.03)^{2x} = 0.5$. Simplifying further, $(0.97)^{2x} = 0.5$. Taking the logarithm of both sides, we can solve for $x$. The exact solution might be complex to find without a calculator, but graphically, we are looking for the $x$-value(s) where the function $500(0.97)^{2x}$ intersects the line $y=250$. The correct answer, rounded to the nearest thousandth if solved accurately, is $x \approx 11.378$, which corresponds to option C.

Solve the Following Graphically 500(1−0.03)2x=250500 ( 1 - 0.03 ) ^ { 2 x } = 250500(1−0.03)2x=250

Solve the Following Graphically $500 ( 1 - 0.03 ) ^ { 2 x } = 250$