Math  /  Math Statement

QuestionIdentify the decreasing exponential function with a yy-intercept of 20 from these options: (1) y=20(43)xy=20\left(\frac{4}{3}\right)^{x} (2) y=20(12)xy=20\left(\frac{1}{2}\right)^{x} (3) y=2x+20y=-2 x+20 (4) y=(13)x+20y=\left(\frac{1}{3}\right)^{x}+20

Studdy Solution
This leaves us with option (2) which is in the form of y=abxy = ab^x where a=20a=20 and b=12b=\frac{1}{2}. When x=0x=0, y=20y=20 which is the y-intercept. And since bb is between0 and1, the function is decreasing.
So, the function that is a decreasing exponential function with a y-intercept of20 is y=20(12)xy=20\left(\frac{1}{2}\right)^{x}.

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