Answer:
Option B (1,10)
Step-by-step explanation:
we have
[tex]f(x)=2(5^x)[/tex]
we know that
If a ordered pair is on the graph of f(x) then the ordered pair must satisfy the function f(x)
Verify each case
case A) (0,0)
For x=0
[tex]f(x)=2(5^0)\\f(x)=2(1)=2[/tex]
Compare the value of f(x) with the y-coordinate of the ordered pair
[tex]2\neq 0[/tex]
therefore
The ordered pair is not on the graph of f(x)
case B) (1,10)
For x=1
[tex]f(x)=2(5^1)\\f(x)=2(5)=10[/tex]
Compare the value of f(x) with the y-coordinate of the ordered pair
[tex]10=10[/tex]
therefore
The ordered pair is on the graph of f(x)
case C) (0,10)
For x=0
[tex]f(x)=2(5^0)\\f(x)=2(1)=2[/tex]
Compare the value of f(x) with the y-coordinate of the ordered pair
[tex]2\neq 10[/tex]
therefore
The ordered pair is not on the graph of f(x)
case D) (10,1)
For x=10
[tex]f(x)=2(5^{10})\\f(x)=2(9,765,625)=19,531,250[/tex]
Compare the value of f(x) with the y-coordinate of the ordered pair
[tex]19,531,250\neq 1[/tex]
therefore
The ordered pair is not on the graph of f(x)
