Question

a computerized video display begins with one polygon on the screen. additional polygons appear on the screen after each second. the graph shows the total number of sides on the screen as a function time. which number is the best estimate for the number of sides on the screen after 3 s? 12 16 24 30

Explanation:

Step1: Analyze the graph

The graph shows the relationship between time (x - axis) and the number of sides (y - axis). We need to estimate the y - value when \(x = 3\).

Step2: Observe the trend

Looking at the points \((1,6)\) and \((4,48)\). The function seems to follow a pattern. If we assume a non - linear growth (since it's not a straight line).
We can also note that from \(x = 1\) to \(x = 4\), the x - values change by \(\Delta x=4 - 1=3\) and the y - values change by \(\Delta y = 48-6 = 42\).
If we consider the interval from \(x = 1\) to \(x = 4\) and try to distribute the growth. But a better way is to look at the position of \(x = 3\) on the x - axis.
When \(x = 3\), by visually inspecting the graph (since it is a curve), we can see that the value of \(y\) (number of sides) is between \(y = 20\) and \(y = 40\).
If we assume a geometric - like growth (since the increase from \(x = 1\) (\(y = 6\)) to \(x = 4\) (\(y = 48\)): \(6\times2^{3}=48\) (where the exponent \(3\) is \(4 - 1\)). For \(x=3\) (from \(x = 1\)), the exponent is \(3 - 1=2\), and \(6\times2^{2}=24\)

Answer:

24