Answer:
Option 2 -The function represent the exponential decay is [tex]f(x) = 4(0.25)^x[/tex]
Step-by-step explanation:
To find : Which function below represents the exponential decay.
Solution :
The exponential function is in the form [tex]y=a(b)^t[/tex]
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) [tex]f(x) = 0.5(2)^x[/tex]
a=0.5 , b=2>1
Exponentially grow
2) [tex]f(x) = 4(0.25)^x[/tex]
a=4 , b=0.25<1
Exponentially decay
3) [tex]f(x) = 2(1.3)^x[/tex]
a=0.5 , b=1.3>1
Exponentially grow
4) [tex]f(x) = (-3)^x[/tex]
a=1 , b=-3 (negative)
Does not exist
Therefore, Option 2 - The function represent the exponential decay is [tex]f(x) = 4(0.25)^x[/tex]
