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Given the following exponential function, identify whether the change represents growth or decay, and determine the percentage rate of increase or decrease.

y=340(0.904)^x

User Voigtan
by
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1 Answer

2 votes

Answer:

  • decay
  • decrease 9.6% per period

Explanation:

You want to know whether the function y = 340(0.904^x) represents growth or decay, and the percentage rate of increase or decrease.

Exponential function

The general form of an exponential function is ...

y = a(b^x)

where ...

  • a = initial value
  • b = growth factor = 1 +growth rate

The function will represent growth when b > 1, and decay when b < 1.

Here, we have ...

b = 0.904 = 1 - 0.096 . . . . . . . . b < 1; growth rate = -9.6%

The function represents decay at the rate of 9.6% per interval.

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Additional comment

No units for x are given, so we don't know what x might represent. It could be seconds, years, decades, or some other sort of interval, such as "iterations." All we know is that when x increases by 1, the value of y decreases by 9.6%.

User John Robins
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3.8k points