SAT Mathematics Practice Test 5

Question : 8 of 58

Marks: +1, -0

In air, the speed of sound S, in meters per second, is a linear function of the air temperature T, indegrees Celsius, and is given by

ST (T)=0.6+331.4.

Which of the following statements is the bestinterpretation of the number

331.4

in this context?

The speed of sound, in meters per second, at $0°$ C
The speed of sound, in meters per second, at $0.6°$ C
The increase in the speed of sound, in meters per second, that corresponds to an increase of $1°$ C
The increase in the speed of sound, in meters per second, that corresponds to an increase of $0.6°$ C

Solution:

The constant term

331.4

S(T)=0.6T+331.4

is the value of S when

T = 0.

The value

T=0

corresponds to a temperature of

0°

C. Since S(T) represents the speed of sound,

331.4

is the speed of sound, in meters per second, when the temperature is

0°

C.
Choice B is incorrect. When

T=0.6°C,S(T)=0.6(0.6)+331.4= 331.76

, not

331.4,

meters per second. Choice C is incorrect. Based on the given formula, the speed of sound increases by

0.6

meters per second for every increase of temperature by

1°

C, as shown by the equation

0.6(T+1)+331.4=(0.6T+331.4)+0.6.

Choice D is incorrect. An increase in the speed of sound, in meters per second, that corresponds to an increase of

0.6°

C is

0.6(0.6)=0.36.

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