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Identify the following exponential function as being growth or decay. f(x)=((3)/(4))^(x)

Identify the following exponential function as being growth or decay.\newlinef(x)=(34)x f(x)=\left(\frac{3}{4}\right)^{x}

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Q. Identify the following exponential function as being growth or decay.\newlinef(x)=(34)x f(x)=\left(\frac{3}{4}\right)^{x}
  1. Exponential Function Form: Understand the general form of an exponential function. An exponential function is generally given by f(x)=axf(x) = a^x, where aa is the base. If a>1a > 1, the function represents exponential growth. If 0<a<10 < a < 1, the function represents exponential decay.
  2. Base Comparison: Compare the base of the given function to 11. The given function is f(x)=(34)xf(x) = (\frac{3}{4})^x. Here, the base is 34\frac{3}{4}, which is less than 11 since 34=0.75\frac{3}{4} = 0.75.
  3. Function Type Determination: Determine if the function represents growth or decay.\newlineSince the base 34\frac{3}{4} is between 00 and 11, the function represents exponential decay.

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