To determine which graph correctly represents the geometric sequence given by the points \( (n, f(n)) \) where:
- \( f(0) = 11 \)
- \( f(1) = 16.5 \)
- \( f(2) = 24.75 \)
- \( f(3) = 37.125 \)
- \( f(4) = 55.6875 \)
we can analyze the \( n \) and \( f(n) \) values:
- For \( n = 0 \), \( f(0) = 11 \)
- For \( n = 1 \), \( f(1) = 16.5 \)
- For \( n = 2 \), \( f(2) = 24.75 \)
- For \( n = 3 \), \( f(3) = 37.125 \)
- For \( n = 4 \), \( f(4) = 55.6875 \)
Next, we note that when \( n \) increases, \( f(n) \) increases as well, indicating that the points are in the first quadrant of the coordinate plane.
- The x-values (n) range from 0 to 4.
- The y-values (f(n)) range from 11 to approximately 55.6875.
Among the options provided, we need to choose the graph where:
- The x-axis ranges from 0 to 6 (to include all x-values we need),
- The y-axis should range from at least 0 to 60 to accommodate the maximum value of \( f(n) \).
The graph that matches these criteria:
- Five points are plotted on the first quadrant of a coordinate plane. The x-axis ranges from 0 to 6 in unit increments and the y-axis ranges from 0 to 60 in increments of 10.
This option covers the relevant ranges for both axes and accurately represents the given geometric sequence.