Question

which function below represents exponential decay?ƒ(x) = 0.5(2)xƒ(x) = 4(0.25)xƒ(x) = 2(1.3)xƒ(x) = (-3)x

Answer 1

Option 2 -The function represent the exponential decay is
`f(x) = 4(0.25)^x`

Explanation:

To find : Which function below represents the exponential decay.

Solution :

The exponential function is in the form
`y=a(b)^t`

where a is the initial value a≠0 and b is the growth or decay factor b>0, b≠0

If the function is exponentially grow then b>1

If the function is exponentially decay then b<1

Now we check given functions by comparing the given exponential function and note the nature of b.

1)
`f(x) = 0.5(2)^x`

a=0.5 , b=2>1

Exponentially grow

2)
`f(x) = 4(0.25)^x`

a=4 , b=0.25<1

Exponentially decay

3)
`f(x) = 2(1.3)^x`

a=0.5 , b=1.3>1

Exponentially grow

4)
`f(x) = (-3)^x`

a=1 , b=-3 (negative)

Does not exist

Therefore, Option 2 - The function represent the exponential decay is
`f(x) = 4(0.25)^x`

Answer 2

the one with the fraction in the parenthasees

remember
F=P(r)^t
in decay, r<1
in growth, r>1
and r is positive so we don't have wierd fliping values

answer would be f(x)=4(0.25)^x

2nd one is answer