Answer: graph E.
A geometric sequence can be written as:
\(a_{n} = a_{1} \cdot r^{(n - 1)}\)
where:
a₁ = first term = 4
r = ratio = 0.5
Substituting the numbers, we have:
\(a_{n} = 4 \cdot (\frac{1}{2})^{n-1}\)
or else
\(f(x) = 4 \cdot (\frac{1}{2})^{x - 1}\)
This is an exponential function with base less than 1. Therefore, we can exclude graph C (which depicts a linear function), and graphs A and D (which depict an exponential function with base greater than 1).
In order to choose between graph B and E, let's evaluate the function in two different points:
\(f(1) = 4 \cdot (\frac{1}{2})^{1 - 1} = 4\)
\(f(2) = 4 \cdot (\frac{1}{2})^{2 - 1} = 4 \cdot \frac{1}{2} = 2\)
Therefore, we need to look for the graph passing through the points (1, 4) and (2, 2). That is graph E.
