Answer:
[tex]f(x) = 4 \times (\dfrac{1}{8})^{x}[/tex].
Step-by-step explanation:
Let [tex]f(x) = a \cdot b^{x}[/tex] represent this exponential function. [tex]a \ne 0[/tex], [tex]b > 0[/tex].
[tex]b^{0} = 1[/tex]. As a result, [tex]a = f(0) = 4[/tex].
[tex]a \cdot b = 4 \cdot b = f(1) = \dfrac{1}{2}[/tex].
As a result,
[tex]b = \dfrac{1}{8}[/tex].
[tex]f(x) = a \cdot b^{x} = 4 \times (\dfrac{1}{8})^{x}[/tex].
This function represents an exponential decay since [tex]0 < b < 1[/tex].
