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Question 2 • 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 a vertex at (0 comma 0), intersects the exponential curve just to the right of the y-axis between y equals 1 and y equals 2, and rises steeply, reaching the top of the grid near x equals 1.5.

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), intersects the exponential curve just to the right of the y-axis between y equals 1 and y equals 2, 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.

Explanation

In choice B, the exponential curve rises more steeply than the quadratic curve: it reaches the top of the grid near x = 1.5, while the quadratic reaches it near x = 4. This shows the exponential is growing faster over the interval from x = 0 to x = 5. The other descriptions show the quadratic rising more steeply than the exponential at least partway through.

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