The table represents an exponential function given by:
[tex]f(x) = 24*(1/2)^x[/tex]
Here we have the table:
x f(x)
0 24
1 12
2 6
3 3
First, notice that for each unit that x increases, the value of f(x) decreases by its half.
This is clearly an exponential equation, whose base must be equal to (1/2).
And because when x = 0, f(0) = 24, we know that the initial value of the function is 24.
Then the exponential function is:
[tex]f(x) = 24*(1/2)^x[/tex]
Such that:
[tex]f(0) = 24*(1/2)^0 = 24\\\\f(1) = 24*(1/2)^1 = 12\\\\f(2) = 24*(1/2)^2 = 24*(1/4) = 6\\\\f(3) = 24*(1/2)^3 = 24*(1/8) = 3[/tex]
Concluding, the table represents an exponential function.
If you want to learn more about exponential functions:
https://brainly.com/question/11464095
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