Exponential Decay Functions — Quiz

Question 1 • Algebra: Concepts and Connections

Which is the graph of f of x is equal to 100 times 0 point 7 to the x th power ?

Answer

Image with description On a coordinate plane, a curve approaches y = 0 in quadrant 1 and curves up into quadrant 2. It goes through (2, 9) and (0, 100).

Image with description On a coordinate plane, a curve approaches y = 0 in quadrant 1 and curves up into quadrant 2. It goes through (2, 30) and (0, 100).

Image with description On a coordinate plane, a curve approaches y = 0 in quadrant 1 and curves up into quadrant 2. It goes through (2, 70) and (0, 100).

Image with description On a coordinate plane, a curve approaches y = 0 in quadrant 1 and curves up into quadrant 2. It goes through (2, 49) and (0, 100).

Explanation

At x = 0, f(0) = 100(0.7)^0 = 100, so the graph passes through (0, 100). At x = 2, f(2) = 100(0.7)^2 = 100(0.49) = 49, so the correct graph is the one passing through (2, 49): choice D.

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