Tell whether the function shows growth or decay. Then graph.
1. f(x) = (1/2)^x 2. f(x) = 1/4(0.25)^x
The exponential function y = a^x increases (models growth) if a>1 and decreases (models decay) if 0 < a < 1.
Since 1/2 = 0.5 < 1, the first function shows decay. The second function is written somewhat unclear.
If f(x) = (1/4) times (0.25)^x, then it shows decay. On the other hand, if f(x) = 1/(4 times 0.25^x), then
f(x) = (1/4) 4^x, and the function shows growth.
Here are the graphs of y = (1/2)^x, of y = (1/4 * (0.25)^x) = (1/4)(0.25)^x, and of y = (1/4)*(0.25)^x.
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