Question

The exponential function
f
(
x
)
=
8
3
(
0.45
)
x
f(x)=
3
8
​
(0.45)
x
represents exponential
growth
while the exponential function
g
(
x
)
=
145
(
1.84
)
x
g(x)=145(1.84)
x
represents
decay

Answer 1

It looks like there may be a misunderstanding regarding the nature of the two exponential functions you've provided.

1. **Exponential Growth**: Generally, an exponential function of the form \( f(x) = ab^x \), where \( b > 1 \), represents exponential growth. In your function \( g(x) = 145(1.84)^x \), since \( 1.84 > 1 \), this function clearly represents exponential growth.

2. **Exponential Decay**: Conversely, an exponential function \( g(x) = ab^x \) where \( 0 < b < 1 \) represents exponential decay. In your function \( f(x) = \frac{3}{8}(0.45)^x \), since \( 0.45 < 1 \), this function represents exponential decay.

Here’s a summary:

- **Function \( f(x) = \frac{3}{8}(0.45)^x \)**: This function represents exponential decay. As \( x \) increases, the value of \( f(x) \) decreases towards 0.

- **Function \( g(x) = 145(1.84)^x \)**: This function represents exponential growth. As \( x \) increases, the value of \( g(x) \) increases without bound.

If you have any further questions about exponential functions or related topics, feel free to ask!