The average monthly temperatures in New Orleans, Louisiana, are given in the following tables:http://postimage.org/image/jvfx3capx/ Applications

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sciencesolve | Teacher | (Level 3) Educator Emeritus

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Considering T(t) the function of temperature, hence, the values comprised by the given table represent the values of T(t). These values form the range of function, hence, the range is the set that comprises all the values from table, taken one time each, such that:

Range = {16.5 ; 18.0 ; 18.3 ; 21.3 ; 21.8 ; 25.6 ; 26.4 ; 29.2 ; 30.3 ; 31.9 ; 32.4 ; 32.6}

There must be 12 values in the range of the function, each value representing the value of corresponding month.

You need to determine the average yearly temperature, hence, you need to evaluate the sum of all the temepratures  above and then, you need to divide this sum to the number of month in a year, 12.

A.Y.T = (16.5 + 18.0 + 18.3 + 21.3 + 21.8 + 25.6 + 26.4 + 29.2+ 30.3 + 31.9 + 32.4 + 32.6)/12

A.Y.T = 304.3/12 => A.Y.T = 25.358

Since the temperature chart presents a cyclical behavior, hence, the temperature function may be modeled by sine function such that:

T(t) = a sin(b(x - c)) + d

You should know if the graph of the function vertically shrinks or stretches by a number of units, then you may find this number of units just looking at the value of a.

The value of b tells you if the graph stretches or shrinks horizontally such that:

- if  0<b<1, then the graph stretches horizontally;

- if b > 1, then the graph shrinks horizontally.

The value of c represents the movement of the graph to the right or to the left, by c units.

Sources:

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