Given the following exponential function, identify whether the change represents growth or decay, and determine the percentage rate of increase or decrease per unit of xx, to the nearest tenth of a percent.y, equals, 4, start superscript, minus, 2, x, end superscripty=4 −2x
Question
Given the following exponential function, identify whether the change represents growth or decay, and determine the percentage rate of increase or decrease per unit of xx, to the nearest tenth of a percent.y, equals, 4, start superscript, minus, 2, x, end superscripty=4 −2x
Solution
The given function is y = 4^(-2x).
This is an exponential decay function because the base of the exponent (4) is positive and the exponent (-2x) is negative.
The rate of decrease per unit of x is 2, but since it's asked in percentage, we convert it by multiplying by 100. So, the percentage rate of decrease per unit of x is 200%.
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