Answer:
Option A is correct.
The function for the given graph is;
[tex]f(x)=2\cdot 4^x[/tex]
Step-by-step explanation:
An exponential function is in the form of [tex]y =ab^x[/tex] ......[1] where a is the initial value and b≠ 0 , b >1 .
Given two points as shown in figure i.e,
let A = (0, 2) and B = (1,8)
Substitute these points in equation [1] we have;
For A = (0,2)
[tex]2 = ab^0[/tex] = a
⇒ a = 2
and
for B = (1, 8)
[tex]8 = ab^1[/tex]
or
[tex]ab = 8[/tex]
Substitute the value of a=2 in above equation to solve for b;
2b = 8
divide both sides by 2 we get;
b = 4
Then, the function for the graph is, y=[tex]f(x)=2\cdot 4^x[/tex]
