which function represents exponential decay?\n$f(x)=\\frac{1}{2}(2)^{x}$\n$f(x)=\\frac{3}{4}(-\\frac{1}{5})^{…

which function represents exponential decay?\n$f(x)=\\frac{1}{2}(2)^{x}$\n$f(x)=\\frac{3}{4}(-\\frac{1}{5})^{x}$\n$f(x)=3(\\frac{7}{2})^{x}$\n$f(x)=2(\\frac{2}{3})^{x}$

which function represents exponential decay?\n$f(x)=\\frac{1}{2}(2)^{x}$\n$f(x)=\\frac{3}{4}(-\\frac{1}{5})^{x}$\n$f(x)=3(\\frac{7}{2})^{x}$\n$f(x)=2(\\frac{2}{3})^{x}$

Answer

Brief Explanations:

An exponential function is of the form (y = a\cdot b^{x}), where (a\neq0). For exponential decay, (0 < b<1).

  • For (f(x)=\frac{1}{2}(2)^{x}), (b = 2>1), so it is exponential growth.
  • For (f(x)=\frac{3}{4}(-\frac{1}{5})^{x}), since the base (b=-\frac{1}{5}) (negative), this is not a valid exponential function (as the base of an exponential function (y = a\cdot b^{x}) should be (b>0,b\neq1)).
  • For (f(x)=3(\frac{7}{2})^{x}), (b=\frac{7}{2}>1), so it is exponential growth.
  • For (f(x)=2(\frac{2}{3})^{x}), (0<\frac{2}{3}<1), so it is exponential decay.

Answer:

(f(x)=2(\frac{2}{3})^{x})