Question

goran is filling a tank with water. the function graphed below shows the amount of water, v(x) (in liters), in the tank x minutes after he started. find v(4) and interpret this value. (a) v(4) = \square (b) the answer to part (a) means there are \square liters in the tank after \square minutes.

Explanation:

Step 1: Identify the graph's axes

The x - axis represents time (in minutes) and the y - axis represents the amount of water \(V(x)\) (in liters). We need to find the value of \(V(4)\), which means we need to find the y - value when \(x = 4\) (time is 4 minutes).

Step 2: Analyze the graph's scale

Looking at the graph, we can assume that the grid lines have a certain scale. From the general shape of the linear graph, we can use the fact that for a linear function \(V(x)=mx + b\), but since we can read from the graph: when \(x = 0\), let's assume the initial value (but we need \(x = 4\)). By looking at the graph, when \(x = 4\) (4 minutes), we can find the corresponding \(y\) - value (amount of water). From the graph (assuming the scale where we can calculate the slope or just read the point), if we consider the two points: let's say at \(x = 0\), \(V(0)=320\) (assuming the top - left point is \((0,320)\)) and at \(x = 18\), \(V(18)=0\). The slope \(m=\frac{0 - 320}{18-0}=-\frac{320}{18}=-\frac{160}{9}\approx - 17.78\). But for \(x = 4\), \(V(4)=320-\frac{160}{9}\times4=320-\frac{640}{9}=\frac{2880 - 640}{9}=\frac{2240}{9}\approx248.89\)? Wait, maybe the graph has a different scale. Wait, maybe the initial point is \((0,320)\) and the end point is \((16,0)\)? Let's recalculate. If \(x = 0\), \(V = 320\) and \(x = 16\), \(V = 0\), then slope \(m=\frac{0 - 320}{16-0}=- 20\). Then \(V(x)=320-20x\). So when \(x = 4\), \(V(4)=320-20\times4=320 - 80 = 240\).

Step 3: Interpret \(V(4)\)

\(V(4)\) represents the amount of water in the tank after 4 minutes. So if \(V(4) = 240\), it means after 4 minutes, there are 240 liters of water in the tank.

Answer:

(for part a):
\(V(4)=\boxed{240}\) (assuming the linear function \(V(x)=320 - 20x\) from the graph's scale, where the tank starts with 320 liters and empties in 16 minutes, so rate of - 20 liters per minute)