Question

Which function represents exponential decay?



y
=
.
8
(
3
)
x
y=.8(3)
x


y
=
3
(
4
)
x
y=3(4)
x


y
=
3
(
.
5
)
x
y=3(.5)
x


y
=
2
(
1.5
)
x
y=2(1.5)
x

Answer 1

To determine which function represents exponential decay, we need to look at the base of the exponential term.

In general, an exponential function can be written as:

\[ y = a(b)^x \]

where:
- \( a \) is a constant,
- \( b \) is the base.

For exponential decay, the base \( b \) must be between 0 and 1 (0 < b < 1).

Now, let's analyze each option:

1. \( y = 0.8(3)^x \)
- Here \( b = 3 \), which is greater than 1. This represents exponential growth, not decay.

2. \( y = 3(4)^x \)
- Here \( b = 4 \), which is also greater than 1. This represents exponential growth.

3. \( y = 3(0.5)^x \)
- Here \( b = 0.5 \), which is between 0 and 1. This represents exponential decay.

4. \( y = 2(1.5)^x \)
- Here \( b = 1.5 \), which is greater than 1. This represents exponential growth.

The correct function that represents exponential decay is:

\[ y = 3(0.5)^x \]