Part 2 of 2
Without graphing, determine whether the function represents exponential growth or exponential decay. Then find the -intercept.

Choose the correct answer below.
The function represents exponential decay.
The function represents exponential growth.
The y-intercept is . (Type an integer or a decimal.)

Ask by Huff Coles. in the United States

Jan 24,2025

Question

Part 2 of 2
Without graphing, determine whether the function represents exponential growth or exponential decay. Then find the -intercept.

Choose the correct answer below.
The function represents exponential decay.
The function represents exponential growth.
The y-intercept is . (Type an integer or a decimal.)

Ask by Huff Coles. in the United States

Jan 24,2025

UpStudy AI · Accepted Answer

The given function is:

$$ f(x) = (0.64)^x $$

### Exponential Growth or Decay

To determine whether the function represents exponential growth or decay, we examine the base of the exponential function:

- **Exponential Growth** occurs when the base $$ b > 1 $$.
- **Exponential Decay** occurs when the base $$ 0 < b < 1 $$.

In this case, the base is $$ 0.64 $$, which is between 0 and 1. Therefore, the function represents **exponential decay**.

### Finding the $$ y $$-Intercept

The $$ y $$-intercept of a function is the value of $$ f(x) $$ when $$ x = 0 $$:

$$ f(0) = (0.64)^0 $$

Any non-zero number raised to the power of 0 is 1:

$$ f(0) = 1 $$

### Final Answer

- **The function represents exponential decay.**
- **The y-intercept is $$ 1 $$.**

Answer:
- The function represents exponential decay.
- The y-intercept is 1.
The function represents exponential decay, and the y-intercept is 1.