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Question 1 • CMS 2026-2027 NC Math 1 CREDIT RECOVERY

For which pair of functions is the exponential consistently growing at a faster rate than the quadratic over the interval 0 is less than or equal to x comma x is less than or equal to 5 ?

Answer

Image with description Coordinate plane with x- and y-axes labeled and a 1-unit grid. An exponential curve crosses the y-axis near 1 and rises steeply, reaching the top of the grid near x equals 1.5. A quadratic curve opens upward with a vertex at (0 comma 0) and rises more gradually, reaching the top of the grid near x equals 4.

Image with description Coordinate plane with x- and y-axes labeled and a 1-unit grid. An exponential curve crosses the y-axis near 1 and rises gradually, reaching the top of the grid near x equals 3. A quadratic curve opens upward with vertex at (0 comma 0) and rises very steeply, reaching the top of the grid near x equals 1.

Image with description Coordinate plane with x- and y-axes labeled and a 1-unit grid. An exponential curve crosses the y-axis near 1 and rises gradually, reaching the top of the grid near x equals 3. A quadratic curve opens upward with a vertex at (0 comma 0), passes near the exponential curve around (1 comma 2), and reaches the top of the grid near x equals 2.

Image with description Coordinate plane with x- and y-axes labeled and a 1-unit grid. An exponential curve crosses the y-axis near 1 and rises gradually, reaching the top of the grid near x equals 3. A quadratic curve opens upward with vertex at (0 comma 0) and rises steeply, reaching the top of the grid near x equals 1.5.

Explanation

An exponential that grows faster should rise more steeply than the quadratic throughout the interval. In choice B, the exponential climbs rapidly and reaches the top of the grid near x = 1.5, while the quadratic rises more gradually and reaches it near x = 4. The other choices show the quadratic rising more steeply or catching up, so they do not fit.

AI-written and checked against the verified answer.

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