Which of the following exponential functions is an increasing function?
Choose the correct answer below

Ask by Munoz Stanley. in the United States

Nov 02,2024

Question

Which of the following exponential functions is an increasing function?
Choose the correct answer below

Ask by Munoz Stanley. in the United States

Nov 02,2024

UpStudy AI · Accepted Answer

To determine which of the given exponential functions is an increasing function, we need to look at the base of each function.

An exponential function of the form $$ f(x) = a^x $$ is increasing if the base $$ a > 1 $$ and decreasing if $$ 0 < a < 1 $$.

Let's analyze each function:

1. $$ f(x) = \left(\frac{3}{2}\right)^{x} $$
   - The base $$ \frac{3}{2} $$ is greater than 1, so this function is increasing.

2. $$ f(x) = \left(\frac{2}{9}\right)^{x} $$
   - The base $$ \frac{2}{9} $$ is less than 1, so this function is decreasing.

3. $$ f(x) = 0.4^{x} $$
   - The base $$ 0.4 $$ is less than 1, so this function is decreasing.

4. $$ f(x) = 0.9^{x} $$
   - The base $$ 0.9 $$ is less than 1, so this function is decreasing.

Based on this analysis, the only increasing function among the options is:

**$$ f(x) = \left(\frac{3}{2}\right)^{x} $$**.
The increasing function is $$ f(x) = \left(\frac{3}{2}\right)^{x} $$.