Question

Barry went scuba diving on his family vacation. The amount of air in his tank steadily changed during his dive.

There is a linear relationship between the time, in minutes, that Barry was diving, and the amount of air in his tank, in cubic feet.

Answer 1

Given that there is a linear relationship between the time Barry spent diving and the amount of air in his tank, we can express this relationship in the form of a linear equation:

\[ A(t) = mt + b \]

Where:
- \( A(t) \) is the amount of air in the tank at time \( t \) (in minutes),
- \( m \) is the rate of change (the slope), which represents how much air is consumed per minute,
- \( b \) is the initial amount of air in the tank (when \( t = 0 \)).

To analyze the situation further, we would need specific values for \( m \) and \( b \). For example, if Barry starts with a full tank of air (let's say \( b = 50 \) cubic feet) and consumes air at a constant rate (for example, \( m = -2 \) cubic feet per minute), the equation would look like this:

\[ A(t) = -2t + 50 \]

Using this equation, we could determine the amount of air left in Barry's tank at any minute during the dive. If Barry dived for \( t = 10 \) minutes, we could calculate:

\[ A(10) = -2(10) + 50 = -20 + 50 = 30 \]

This means after 10 minutes of diving, Barry would have 30 cubic feet of air left in his tank.

If you provide specific values for the start amount of air and the consumption rate, I can help you calculate specific instances or further analyze the situation!