which function is a shrink of the exponential growth function shown on the graph?\n$f(x)=2(3)^{x}$\n$f(x)=\\f…

which function is a shrink of the exponential growth function shown on the graph?\n$f(x)=2(3)^{x}$\n$f(x)=\\frac{1}{2}(3)^{x}$\n$f(x)=2(\\frac{1}{3})^{x}$\n$f(x)=\\frac{1}{2}(\\frac{1}{3})^{x}$

which function is a shrink of the exponential growth function shown on the graph?\n$f(x)=2(3)^{x}$\n$f(x)=\\frac{1}{2}(3)^{x}$\n$f(x)=2(\\frac{1}{3})^{x}$\n$f(x)=\\frac{1}{2}(\\frac{1}{3})^{x}$

Answer

Explanation:

Step1: Recall the form of exponential growth function

The general form of an exponential growth function is (y = a\cdot b^{x}), where (a>0) and (b > 1).

Step2: Analyze each option

  • For (f(x)=2(3)^{x}): Here (a = 2) and (b=3). This is a vertical stretch (since (a = 2>1)) of (y=(3)^{x}).
  • For (f(x)=\frac{1}{2}(3)^{x}): Here (a=\frac{1}{2}) and (b = 3). Since (0<a=\frac{1}{2}<1), this is a vertical shrink of (y=(3)^{x}).
  • For (f(x)=2(\frac{1}{3})^{x}): Here (b=\frac{1}{3}<1), so it is an exponential decay function.
  • For (f(x)=\frac{1}{2}(\frac{1}{3})^{x}): Here (b=\frac{1}{3}<1), so it is an exponential decay function.

Answer:

(f(x)=\frac{1}{2}(3)^{x})