Answer:
[tex]f(x)=20(2.5^x)[/tex]
Step-by-step explanation:
we know that
The function of the graph is a exponential function of the form
[tex]f(x)=a(b^x)[/tex]
Looking at the graph
we have the points
(0,20) and (1,50)
Remember that if a point lie on the graph, then the point must satisfy the function
Verify each case
For x=1, f(x)=50
case 1) we have
[tex]f(x)=20(1.5^x)[/tex]
For x=1
[tex]f(1)=20(1.5^1)=30[/tex]
so
[tex]30\neq 50[/tex]
therefore
This function is not represented by the graph
case 2) we have
[tex]f(x)=20(1.4^x)[/tex]
For x=1
[tex]f(1)=20(1.4^1)=28[/tex]
so
[tex]28\neq 50[/tex]
therefore
This function is not represented by the graph
case 3) we have
[tex]f(x)=20(2.5^x)[/tex]
For x=1
[tex]f(1)=20(2.5^1)=50[/tex]
[tex]50=50[/tex]
For x=0
[tex]f(0)=20(2.5^0)=20[/tex]
[tex]20=20[/tex]
therefore
This function is represented by the graph
case 4) we have
[tex]f(x)=20(2.25^x)[/tex]
For x=1
[tex]f(1)=20(2.25^1)=45[/tex]
so
[tex]45\neq 50[/tex]
therefore
This function is not represented by the graph
