which is a stretch of an exponential growth function?\n$f(x)=\frac{2}{3}(\frac{2}{3})^x$\n$f(x)=\frac{3}{2}(\…

Explanation:

Step1: Recall exponential - growth form

The general form of an exponential function is (y = ab^{x}), where (a\neq0), (b > 0), and (b\neq1). For an exponential growth function, (b>1).

Step2: Analyze each option

• For (f(x)=\frac{2}{3}(\frac{2}{3})^{x}), (a = \frac{2}{3}) and (b=\frac{2}{3}<1), so it is an exponential decay function.
• For (f(x)=\frac{3}{2}(\frac{2}{3})^{x}), (a=\frac{3}{2}) and (b = \frac{2}{3}<1), so it is an exponential decay function.
• For (f(x)=\frac{3}{2}(\frac{3}{2})^{x}), (a=\frac{3}{2}) and (b=\frac{3}{2}>1), so it is an exponential growth function.
• For (f(x)=\frac{2}{3}(\frac{3}{2})^{x}), (a=\frac{2}{3}) and (b=\frac{3}{2}>1), so it is an exponential growth function. Among them, (y = \frac{3}{2}(\frac{3}{2})^{x}) has a larger coefficient (a=\frac{3}{2}) compared to (y=\frac{2}{3}(\frac{3}{2})^{x}), which means it is a stretch of the basic exponential - growth function (y = (\frac{3}{2})^{x}).

Answer:

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