Answer:
[tex]y = 2(2) {}^{x} [/tex]
Step-by-step explanation:
It ask us to create a exponential function. A exponential function is represented by a equation like this
[tex]y = ab {}^{x} [/tex]
where a is the vertical stretch, b is the constant rate of growth, and x is the nth exponet.
Using the point 0,2
we can plug that in to find a part of the equation above.
let x=0 and y=2
[tex]2 = ab {}^{0} [/tex]
[tex]b {}^{0} = 1[/tex]
[tex]2 = a \times 1[/tex]
[tex]a = 2[/tex]
Let update the equation now since a equal 2
[tex]y = 2b {}^{x} [/tex]
Now let use point 2,8 to find the b value
let x=2 and y=8
[tex]8 = 2b {}^{2} [/tex]
Divide both sides by 2
[tex]4 = {b}^{2} [/tex]
take the sqr root of 4
[tex]b = 2[/tex]
Let update the equation
[tex]y = 2(2) {}^{x} [/tex]
