Respuesta :
Answer:
The function representing exponential decay are:
b) [tex]f(x)=(0.85)^{x}[/tex]
d) [tex]f(x)=1.8(0.6)^{x}[/tex]
e) [tex]f(x)=(0.95)^{2x}[/tex]
Step-by-step explanation:
The exponential function is given as:
[tex]f(x)=ab^x[/tex]
where [tex]a\neq 0[/tex], [tex]b\neq 1[/tex], and [tex]b > 0[/tex].
If [tex]a>0[/tex] and [tex]0<b<1[/tex] then the function represents exponential decay.
If [tex]a>0[/tex] and [tex]b>1[/tex] then the function represents exponential growth.
Thus, we can check each function given.
a) [tex]f(x)=0.25(1.5)^{3x}[/tex]
For the given function [tex]a=0.25>0[/tex] and [tex]b=1.5>1[/tex]. So, it represents exponential growth.
b) [tex]f(x)=(0.85)^{x}[/tex]
For the given function [tex]a=1>0[/tex] and [tex]0<b=0.85<1[/tex]. So, it represents exponential decay.
c) [tex]f(x)=(1.01)^{x}[/tex]
For the given function [tex]a=1>0[/tex] and [tex]b=1.01>1[/tex]. So, it represents exponential growth.
d) [tex]f(x)=1.8(0.6)^{x}[/tex]
For the given function [tex]a=1.8>0[/tex] and [tex]0<b=0.6<1[/tex]. . So, it represents exponential decay.
e) [tex]f(x)=(0.95)^{2x}[/tex]
For the given function [tex]a=1>0[/tex] and [tex]0<b=0.95<1[/tex]. . So, it represents exponential decay.
