Exponential and Logarithmic Functions — Test

Question 19 • Algebra 2 with Probability

Which graph represents an exponential decay function?

Answer

Image with description On a coordinate plane, the x-axis is labeled 'x' and ranges from negative 10 to 10. The y-axis is labeled 'y' and ranges from negative 10 to 10. A curved line, begins at the origin (0 comma 0) and extends into the first quadrant. The curve is continuously increasing and appears concave down. It passes through (1 comma 1), (3 comma 2), and (8 comma 3).

Image with description On a coordinate plane, the x-axis is labeled 'x' and ranges from negative 10 to 10. The y-axis is labeled 'y' and ranges from negative 10 to 10. A curved line, passes through the points (negative 2 comma 0 point 2 5), (negative 1 comma 0 point 5), (0 comma 1), (1 comma 2), (2 comma 4) and (3 comma 8). The curve has a horizontal asymptote at y equals 0 (the x-axis), which it approaches as x approaches negative infinity.

Image with description On a coordinate plane, the x-axis is labeled 'x' and ranges from negative 10 to 10. The y-axis is labeled 'y' and ranges from negative 10 to 10. A curved line, begins at approximately (0 comma 0) and extends to the right in fourth quadrant. The curve is continuously decreasing and it passes through approximately (1 comma negative 1), (4 comma negative 2), and (9 point 5 comma negative 3).

Image with description On a coordinate plane, the x-axis is labeled 'x' and ranges from negative 10 to 10. The y-axis is labeled 'y' and ranges from negative 10 to 10. A curved line, passes through the points (negative 1 comma 2), (negative 2 comma 4), (negative 3 comma 8), (0 comma 1), (1 comma 0 point 5), and (2 comma 0 point 2 5). The curve has a horizontal asymptote at y equals 0 (the x-axis), which it approaches as x approaches positive infinity.

Explanation

An exponential decay function gets smaller as x increases, approaching a horizontal asymptote. In graph B, the y-values halve as x increases by 1: for example, y goes from 1 at x = 0 to 0.5 at x = 1 and 0.25 at x = 2. So B represents exponential decay.

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