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.
