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ANSWER
The answer is D

[tex]f(x) = 4{(0.5)}^{x} [/tex]

EXPLANATION

Let the exponential function be of the form

[tex]f(x) = a {b}^{x} [/tex]

Each box on both the x and y axes is one unit.

The graph passes through the point [tex](0,4) [/tex].

This point must satisfy the equation above.

[tex]4 = a {b}^{0} [/tex]

This implies that,

[tex]4 = a(1)[/tex]

[tex]a = 4[/tex]

The function now becomes,

[tex]f(x) = 4 {(b})^{x} [/tex]

The graph also passes through

[tex](1,2).[/tex]

We substitute this point too to get,

[tex]2 = 4 {b}^{1} [/tex]

This implies that,

[tex]2 = 4b[/tex]

[tex]b = \frac{2}{4} [/tex]

[tex]b = \frac{1}{2} [/tex]

or

[tex]b = 0.5[/tex]

We substitute back to get,

[tex]f(x) = 4 {(0.5})^{x} [/tex]

The correct answer is D.

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