Question

The table shows the speeds s (in feet per second) of sound in water at various

temperatures t (in degrees Fahrenheit). Write a function that models the data. Use
the model to approximate the speed of sound when the water temperature is 100°F.
Temperature (°F), t: 32 50 90 120 180 212
Speed (ft/sec), s: 4603 4748 4960 5049 5095 5062

Answer 1

To model the data, we can use a linear function relating temperature to the speed of sound in water. Using the equation s = 2.488t + 4565.96, we can approximate the speed of sound when the water temperature is 100°F to be 4806.96 feet per second.

Step-by-step explanation:

To model the data, we need to find a function that relates the temperature to the speed of sound in water.

One common model for this relationship is a linear function.

We can use the temperature values as the independent variable and the speed of sound values as the dependent variable. Let's use the points (32, 4603), (50, 4748), (90, 4960), (120, 5049), (180, 5095), and (212, 5062) to find the equation of the line.

Using the method of least squares, we find that the equation of the line is s = 2.488t + 4565.96, where s is the speed of sound in feet per second and t is the temperature in degrees Fahrenheit.

To approximate the speed of sound when the water temperature is 100°F, we can plug t = 100 into the equation and solve for s.

Substituting t = 100 into the equation, we get s = 2.488(100) + 4565.96 = 4806.96 feet per second.