Respuesta :
Answer:
[tex]f(x)=\frac{1}{2}(6)^x[/tex]
Step-by-step explanation:
An exponential function is of the form [tex]y=ab^{x}[/tex], where,[tex]a\ne 0[/tex].
Now, if a > 0 and b > 1, then the exponential function represent exponential growth.
If a > 0 and 0 < b < 1, then the exponential function represent exponential decay.
Let us check each function now.
Option 1: [tex]f(x)=4(0.07)^x[/tex]
Here, [tex]a=4,b=0.07[/tex]
As 0.07 < 1, the function is exponential decay.
Option 2: [tex]f(x)=2(0.44)^x[/tex]
Here, [tex]a=2,b=0.44[/tex]
As 0.44 < 1, the function is exponential decay.
Option 3: [tex]f(x)=\frac{1}{2}(6)^x[/tex]
Here, [tex]a=\frac{1}{2},b=6[/tex]
As 6 > 1, the function is exponential growth.
Option 4: [tex]f(x)=7(\frac{1}{2})^x[/tex]
Here, [tex]a=7,b=\frac{1}{2}[/tex]
As [tex]\frac{1}{2}< 1[/tex], the function is exponential decay.
Therefore, the equation that represent exponential growth is [tex]f(x)=\frac{1}{2}(6)^x[/tex]
