Marine scientists use a linear model for the speed c of sound in the oceans as a function of the salinity S at a fixed depth and temperature.† In the following table, one scientist recorded data for c and S at a depth of 500 meters and a temperature of 15 degrees Celsius. Here c is measured in meters per second and S in parts per thousand. Salinity S Sound speed c 35.0 1515.36 35.6 1516.08 36.2 1516.80 36.8 1517.62 37.4 1518.24 (a) Looking over the table, the scientist realizes that one of the entries for sound speed is in error. Which entry is it? S = What is the correct speed? c = m/sec (b) Explain in practical terms the meaning of the slope of the linear model for c in terms of S at the given depth and temperature. The slope means that, at the given depth and temperature, for an increase in salinity of part per thousand the speed of sound increases by meters per second. (c) Calculate c(38.2). c(38.2) = m/sec Explain in practical terms what it means. This means that the speed of sound is meters per second when the salinity is parts per thousand.
Marine scientists use a linear model for the speed c of sound in the oceans as a function of the salinity S at a fixed depth and temperature.† In the following table, one scientist recorded data for c and S at a depth of 500 meters and a temperature of 15 degrees Celsius. Here c is measured in meters per second and S in parts per thousand. Salinity S Sound speed c 35.0 1515.36 35.6 1516.08 36.2 1516.80 36.8 1517.62 37.4 1518.24 (a) Looking over the table, the scientist realizes that one of the entries for sound speed is in error. Which entry is it? S = What is the correct speed? c = m/sec (b) Explain in practical terms the meaning of the slope of the linear model for c in terms of S at the given depth and temperature. The slope means that, at the given depth and temperature, for an increase in salinity of part per thousand the speed of sound increases by meters per second. (c) Calculate c(38.2). c(38.2) = m/sec Explain in practical terms what it means. This means that the speed of sound is meters per second when the salinity is parts per thousand.
Functions and Change: A Modeling Approach to College Algebra (MindTap Course List)
6th Edition
ISBN:9781337111348
Author:Bruce Crauder, Benny Evans, Alan Noell
Publisher:Bruce Crauder, Benny Evans, Alan Noell
Chapter3: Straight Lines And Linear Functions
Section3.3: Modeling Data With Linear Functions
Problem 19E: Sound Speed in Oceans Marine scientists use a linear model for the speed c of sound in the oceans as...
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Marine scientists use a linear model for the speed c of sound in the oceans as a function of the salinity S at a fixed depth and temperature.† In the following table, one scientist recorded data for c and S at a depth of 500 meters and a temperature of 15 degrees Celsius. Here c is measured in meters per second and S in parts per thousand.
| Salinity S | Sound speed c |
|---|---|
| 35.0 | 1515.36 |
| 35.6 | 1516.08 |
| 36.2 | 1516.80 |
| 36.8 | 1517.62 |
| 37.4 | 1518.24 |
(a) Looking over the table, the scientist realizes that one of the entries for sound speed is in error. Which entry is it?
S =
What is the correct speed?
c = m/sec
(b) Explain in practical terms the meaning of the slope of the linear model for c in terms of S at the given depth and temperature.
(c) Calculate c(38.2).
c(38.2) = m/sec
Explain in practical terms what it means.
S =
What is the correct speed?
c = m/sec
(b) Explain in practical terms the meaning of the slope of the linear model for c in terms of S at the given depth and temperature.
The slope means that, at the given depth and temperature, for an increase in salinity of part per thousand the speed of sound increases by meters per second.
(c) Calculate c(38.2).
c(38.2) = m/sec
Explain in practical terms what it means.
This means that the speed of sound is meters per second when the salinity is parts per thousand.
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