Question

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

Answer 1

The function \( f(x) = \frac{3}{8} (0.45)^x \) represents an exponential decay, because the base \( 0.45 \) is less than 1. This means that as \( x \) increases, \( f(x) \) will decrease towards 0.

On the other hand, the function \( g(x) = 145 (1.84)^x \) represents an exponential growth, because the base \( 1.84 \) is greater than 1. This means that as \( x \) increases, \( g(x) \) will increase without bound.

In summary:
- \( f(x) = \frac{3}{8} (0.45)^x \): Exponential decay
- \( g(x) = 145 (1.84)^x \): Exponential growth