To the nearest hundredth, what is the positive solution of $2.4^x=7-x$?

Answer and derivation

Correct answer: C

The graphs intersect at approximately $x=1.87$.

1. Enter both sides as separate functions.
2. Locate the only crossing in the positive window.
3. The x-coordinate is about $1.868$, which rounds to $1.87$.

Why the other options fail

A

This results from an early rough visual estimate.

B

This can result from using an inaccurate table step.

C

Correct numerical intersection and rounding.

D

It copies the exponential base.

Common misconception: A graphing result should identify the equation and report the requested coordinate and precision.

China/AP bridge: China-course bridge: numerical equation solving extends graph intersections; AP expects technology use plus written equation and precision; unlike relying on pixel reading, use the intersect feature; avoid typing multiplication in place of exponentiation.