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Question 7 • CMS 2026-2027 NC Math 1 CREDIT RECOVERY

Which graph represents exponential decay?

Answer

Image with description A coordinate plane with a horizontal x-axis labeled from negative 4 to 6 and a vertical y-axis labeled from negative 1 to 9 in increments of 1. The curve begins in the second quadrant near the coordinate point negative 2 comma 0 with a downward-pointing arrowhead touching the x-axis at negative 2. From this point, it curves steeply upwards and to the right, crossing through the point negative 1 comma 4 and the y-axis at 0 comma 4 point 5. It then curves more gradually into the first quadrant, passing near the point 2 comma 5 and continuing towards the right to an arrowhead pointing near 6 comma 5 point 7.

Image with description A coordinate plane with a horizontal x-axis labeled from negative 4 to 6 and a vertical y-axis labeled from negative 1 to 9 in increments of 1. The curve passes through the coordinate point negative 1 comma 3, and extends upwards to negative 2 comma 9. The curve decreases sharply downwards, crossing the y-axis at 0 comma 1. It then enters the first quadrant, passing near 1 comma 0 point 3 and flattening along the x-axis.

Image with description A coordinate plane with a horizontal x-axis labeled from negative 4 to 6 and a vertical y-axis labeled from negative 1 to 9 in increments of 1. The curve starts flat near the x-axis in the second quadrant with an arrowhead pointing near negative 3 point 5 comma 0. Moving from left to right, it passes through negative 1 comma 0 point 3, crosses the y-axis at 0 comma 1, and enters the first quadrant. As it moves further right, it grows steeply upwards, passing through 1 comma 3, and continuing upwards to an arrowhead pointing near 2 comma 9.

Image with description A coordinate plane with a horizontal x-axis labeled from negative 4 to 6 and a vertical y-axis labeled from negative 1 to 9 in increments of 1. A linear function shown as a straight line is plotted on the grid. The line has a negative slope, passing through the y-axis at 0 comma 1 and the x-axis near 0 point 5 comma 0. It extends upwards into the second quadrant, passing through the coordinate point negative 1 comma 3, and continuing upwards to an arrowhead pointing near negative 4 comma 9. It extends downwards into the fourth quadrant with an arrowhead pointing near 1 comma negative 1.

Explanation

Exponential decay decreases as x increases, typically dropping quickly at first and then leveling off toward the x-axis. Graph B has that shape: it passes through (−2, 9), (−1, 3), and (0, 1), then continues downward toward the x-axis as x increases. Graph C instead shows exponential growth, and D is a straight line.

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