Given the following exponential function, identify whether the change represents growth or decay, and determine the percentage rate of increase or decrease.y, equals, 4600, left bracket, 0, point, 9, 6, right bracket, to the power xy=4600(0.96) x
Question
Given the following exponential function, identify whether the change represents growth or decay, and determine the percentage rate of increase or decrease.y, equals, 4600, left bracket, 0, point, 9, 6, right bracket, to the power xy=4600(0.96) x
Solution
The given function is y = 4600(0.96)^x.
Step 1: Identify Growth or Decay The base of the exponent in the function is 0.96. Since this value is less than 1, the function represents decay, not growth.
Step 2: Determine the Rate of Decrease The rate of decrease is determined by subtracting the base of the exponent from 1 and multiplying by 100 to convert it to a percentage.
So, Rate of decrease = (1 - 0.96) * 100 = 0.04 * 100 = 4%
Therefore, the function represents a 4% rate of decay.
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