Determine whether the equation below is exponential growth or decay. $$ f(x)=\left(\frac{2}{5}\right)^{x} $$ growth decay

Question

UpStudy AI · Accepted Answer

1. Recognize the standard exponential form:
   $$
   f(x)=a^x
   $$
   where $$ a $$ is the base of the exponential function.

2. In our given equation, the base is:
   $$
   a=\frac{2}{5}
   $$

3. Since the base is positive and satisfies:
   $$
   0 < a < 1
   $$
   this indicates that the function is exponentially decaying.

4. Hence, the equation represents:

**decay**.
The equation $$ f(x)=\left(\frac{2}{5}\right)^{x} $$ represents **decay**.

Determine whether the equation below is exponential growth or decay. \( f(x)=\left(\frac{2}{5}\right)^{x} \) growth decay