Question

Which function represents exponential decay?



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


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


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


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

Answer 1

In exponential decay, the function typically has a base that is between 0 and 1. To identify which function represents exponential decay from the options provided, we should look for a base less than 1.

1. **y = 2(1.5)^x** — Base is 1.5 (greater than 1, represents exponential growth)
2. **y = 3(4)^x** — Base is 4 (greater than 1, represents exponential growth)
3. **y = .8(3)^x** — Base is 3 (greater than 1, represents exponential growth)
4. **y = 3(0.5)^x** — Base is 0.5 (less than 1, represents exponential decay)

Thus, the function that represents exponential decay is:

**y = 3(0.5)^x**.