On khan academy the answer is g(x)=12([tex]\frac{1}{6}[/tex])^x
:)
The required exponential function will be g(x) = a.bˣ = 12×([tex]\frac{3}{4}[/tex])ˣ.
"An exponential function is defined by the formula f(x) = ax, where the input variable x occurs as an exponent. The exponential curve depends on the exponential function and it depends on the value of the x. The exponential function is an important mathematical function which is of the form. f(x) = ax."
Given function, g(x) = abˣ
Now, for x = 0; g(x) = 12. For, x = 1; g(x) = 9.
By putting x = 0 in the function g(x), we get:
⇒ g(0) = 12
⇒ a.b⁰ = 12
⇒ a = 12
Again, putting x = 1 in the function g(x), we get:
⇒ g(1) = 9
⇒ a. b¹ = 9
⇒ 12 b = 9
⇒ b = [tex]\frac{9}{12}[/tex]
⇒ b = [tex]\frac{3}{4}[/tex]
Therefore, the required exponential function, g(x) = a.bˣ = 12×([tex]\frac{3}{4}[/tex])ˣ
Learn more about exponential function here: https://brainly.com/question/15352175
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