which is a stretch of an exponential decay function?\n f(x)=\frac{4}{5}(\frac{5}{4})^x \n f(x)=\frac{4}{5}(\f…

Answer:

C. $f(x)=\frac{5}{4}(\frac{4}{5})^x$

Explanation:

Step1: Recall exponential - decay form

The general form of an exponential function is $y = ab^x$, where $a\neq0$, $b > 0$, and $b\neq1$. For an exponential decay function, $0 < b<1$.

Step2: Analyze each option

• Option A: In $f(x)=\frac{4}{5}(\frac{5}{4})^x$, since $\frac{5}{4}>1$, it is an exponential growth function.
• Option B: In $f(x)=\frac{4}{5}(\frac{4}{5})^x$, the base $\frac{4}{5}\in(0,1)$ but the coefficient $\frac{4}{5}<1$, it is a non - stretched exponential decay function.
• Option C: In $f(x)=\frac{5}{4}(\frac{4}{5})^x$, the base $\frac{4}{5}\in(0,1)$ and the coefficient $\frac{5}{4}>1$, so it is a stretched exponential decay function.
• Option D: In $f(x)=\frac{5}{4}(\frac{5}{4})^x$, since $\frac{5}{4}>1$, it is an exponential growth function.