Determine whether each function represents exponential growth or decay. Write the base in terms of the rate of growth or decay, identify r, and interpret the rate of growth or decay f(x)=12000(710)x

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Determine whether each function represents exponential growth or decay. Write the base in terms of the rate of growth or decay, identify r, and interpret the rate of growth or decay  f(x)=12000(710)x

ocretz56 · Accepted Answer

For an exponential function in the form&amp;nbsp;y=a×bx&amp;nbsp;If&amp;nbsp;b&amp;gt;1, the function is increasing and is an exponential growth function.&amp;nbsp;If&amp;nbsp;0&amp;lt;b&amp;lt;1, the function is decreasing and is an exponential decay function.&amp;nbsp;Because&amp;nbsp;b=710&amp;lt;1, then the function represents an exxponential decay&amp;nbsp;The exponential decay function is given by:&amp;nbsp;A(t)=a(1−r)t&amp;nbsp;where a is the initial amount, (1 - r) is the decay factor, and r is the rate of decay.&amp;nbsp;Using the value of b,&amp;nbsp;b=1−r→710=1−310&amp;nbsp;Hence, the base in terms of the rate of decay is:&amp;nbsp;f(x)=12000(1−310)x&amp;nbsp;and r is the rate of decay:&amp;nbsp;r=310=0.3&amp;nbsp;or&amp;nbsp;30%&amp;nbsp;This means that the function decreases by 30% as x increases by 1&amp;nbsp;exponential decay;&amp;nbsp;f(x)=12000(1−310)x;r=310=0.3&amp;nbsp;or&amp;nbsp;30%

Determine whether each function represents exponential growth or decay. Write

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