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Chapter 3: Problem 28

The water temperature of the Pacific Ocean varies inversely as the water's depth. At a depth of 1000 meters, the water temperature is \(4.4^{\circ}\) Celsius. What is the water temperature at a depth of 5000 meters?

Short Answer

Expert verified
The water temperature at a depth of 5000 meters will be approximately \(0.88^{\circ}\) Celsius.

Step by step solution

01

- Establishing the equation of inverse proportion

Given the problem, the equation illustrating the inverse proportion can be written as \( T = \frac{k}{D} \), where \(\T\) is the temperature in degrees Celsius and \(D\) is the depth in meters. \(\k\ is a constant which we need to find.
02

- Find the constant of variation (k)

At a depth of 1000 meters, the water temperature is \(4.4^{\circ}\) Celsius. We can substitute these values into the equation to find \(k\): \[ k = TD \ k = 1000 * 4.4 \ k = 4400 \]
03

- Use the constant to find the temperature at a depth of 5000 meters

To find the temperature at a depth of 5000 meters, we can substitute the values of \(D = 5000\) and \( k = 4400 \) in the equation: \[ T = \frac{k}{D} \ T = \frac{4400}{5000} \]

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