Question

Given the following exponential function, identify whether the change represents growth or decay, and determine the percentage rate of increase or decrease.
y=290(0.31)^x

Answer 1

The exponential function y = 290 · 0.31ˣ reports a decay as its growth rate is less than 1 and greater than 0. Its percentage rate of decrease is equal to 69 %.

How to determine the behavior of an exponential function

Exponential functions are trascendental functions, these are, functions that cannot be described algebraically. The simplest form of exponential functions is shown below:

y = a · bˣ     (1)

Where:

• a - Initial value
• b - Growth rate
• x - Independent variable.
• y - Dependent variable.

Please notice that this kind of exponential function reports a growth for b > 1 and decay for b < 1 and b > 0. According to the statement we have the function y = 290 · 0.31ˣ, then we conclude that the exponential function given reports a decay.

The percentage rate of decrease is determined by the following formula:

100 × (1-0.31) = 100 × 0.69 = 69 %

The percentage rate of decrease related to the exponential function is 69 %.

To learn more on exponential functions: brainly.com/question/11487261

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