Answer:
So, only option-c and option-d are same
Step-by-step explanation:
(a) From Graph:
Firstly, we will find function of the graph
Let's assume exponential function as
[tex]f(x)=a(b)^x[/tex]
we can select any two points and find 'a' and 'b'
[tex]f(0)=\frac{1}{2}[/tex]
At x=0 , y=1/2:
we can plug values
[tex]f(0)=a(b)^0[/tex]
[tex]\frac{1}{2}=a(b)^0[/tex]
[tex]a=\frac{1}{2}[/tex]
now, we can plug it back
and we get
[tex]f(x)=\frac{1}{2}(b)^x[/tex]
At x=-1 , y=2:
we can plug values
[tex]f(-1)=\frac{1}{2}(b)^{-1}[/tex]
[tex]2=\frac{1}{2}(b)^{-1}[/tex]
[tex]b=\frac{1}{4}[/tex]
now, we can plug it back
and we get
[tex]f(x)=\frac{1}{2}(\frac{1}{4})^x[/tex]
(b) From chart:
Firstly, we will find function of the graph
Let's assume exponential function as
[tex]f(x)=a(b)^x[/tex]
we can select any two points and find 'a' and 'b'
[tex]f(0)=\frac{1}{2}[/tex]
At x=0 , y=1/2:
we can plug values
[tex]f(0)=a(b)^0[/tex]
[tex]\frac{1}{2}=a(b)^0[/tex]
[tex]a=\frac{1}{2}[/tex]
now, we can plug it back
and we get
[tex]f(x)=\frac{1}{2}(b)^x[/tex]
At x=1 , y=1:
we can plug values
[tex]f(1)=\frac{1}{2}(b)^{1}[/tex]
[tex]1=\frac{1}{2}(b)^{1}[/tex]
[tex]b=2[/tex]
now, we can plug it back
and we get
[tex]f(x)=\frac{1}{2}(2)^x[/tex]
