Solve the equation $\frac { 20 } { 1 + 2 ^ { x } } = x$ Restrict your attention to the horizontal span of 0 to 5.
A) 4.89
B) 3.14
C) 2.69
D) 4.17

Question

Quizplus · Accepted Answer

First, notice that $x=0$ is not a solution because we would have division by zero. Also, observe that as $x$ gets very large, the denominator, $1+2^x$, of the fraction gets very close to $2^x$. Therefore, the fraction gets very close to $\frac{20}{2^x}$, which approaches 0 as $x$ gets very large. This suggests that there is at least one solution. Graphing the function $y=\frac{20}{1+2^x}$ and $y=x$ on the same set of axes, we see that the two graphs intersect once between 2 and 3. This intersection occurs at approximately $x=2.69$, so the answer is $\boxed{	extbf{(C)}}$.

Note: It is also possible to use Calculus methods to show that there is exactly one solution between the given interval, but this is not necessary for answering the question.

Solve the Equation 201+2x=x\frac { 20 } { 1 + 2 ^ { x } } = x1+2x20​=x

Solve the Equation $\frac { 20 } { 1 + 2 ^ { x } } = x$