The maximum time, T, in minutes, a scuba diver can rise without stopping for decompression on the way to the surface is modeled by the equation T (d) = 525/d-10 , d > 10, where d is the depth of the dive in metres.
a) sketch a graph of this relationship.
b) use the graph to show how deep a diver can dive for the maximum time to be less than 30 min.
To sketch a graph of the relationship T(d) = 525/(d - 10), where d is the depth of the dive in meters, we can follow these steps:
1. Determine the domain: The equation states that d should be greater than 10, so the domain of the function is {d ∈ ℝ | d > 10}.
2. Identify key points: We can start by identifying some key points to plot on the graph.
- At d = 11, the time would be T(11) = 525/(11 - 10) = 525 minutes.
- At d = 20, the time would be T(20) = 525/(20 - 10) = 52.5 minutes.
- At d = 30, the time would be T(30) = 525/(30 - 10) = 21 minutes.
3. Plot the points: Plot the points (11, 525), (20, 52.5), and (30, 21) on the graph.
4. Draw the graph: Since we know that the function approaches infinity as d approaches 10, we can draw a vertical asymptote at d = 10, which means the graph should not touch or cross this line.
Here is a rough sketch of the graph:
|
| .
| .
| .
| .
| .
---------+----------------
|
10
Now, to determine how deep a diver can go for the maximum time to be less than 30 minutes, we analyze the graph:
1. Look at the graph and the points plotted: From the graph, we can see that when the time T is less than 30 minutes, the diver's depth d is restricted to approximately less than or equal to 30 meters.
2. Interpretation: The graph indicates that a diver can dive up to approximately 30 meters deep without the maximum time, T, exceeding 30 minutes.
Therefore, based on the graph, the maximum depth for the maximum time to be less than 30 minutes is approximately 30 meters.