The date of the first sighting of robins has been occurring earlier each spring

Question

The date of the first sighting of robins has been occurring earlier each spring over the past 25 years at a certain laboratory. Scientists from this laboratory have developed two linear equations, shown below, that estimate the date of the first sighting of robins, where x is the year and y is the estimated number of days into the year when a robin can be expected. Complete parts a and b.

(Hint: 2000 was a leap year.)

y

=

7020.318x

y

=

16420.781x

a. Compare the date of first sighting in 2000 for each of these equations.

March 11, March 29

March 7, March 21

March 6, March 20

March 26, March 10

b. Solve this system of equations to find the year in which the two estimates agree.                          (Round to the nearest year as needed.)

y

=

7020.318x

y

=

16420.781x

Explanation / Answer

FROM FIRST EQUATION NUMBER OF DAYS ROBIN WAS SEEN IN YEAR 2000 IS

Y = 702 - 0.318* 2000 = 702 - 636 = 66 DAYS

FROM SECOND EQATION Y = 1642 - 0.781* 2000 = 1642 - 1562 = 80 DAYS , DIFFERENCE IN DAYS = 80 - 66

= 14 DAYS

(a) COMPARING BOTH FIRST SIGHTING DATE MUST BEEITHER ' MARCH 21' FOR FIRST AND 'MARCH 7' FOR SECOND OR 'MARCH 20 FOR FIRST AND 'MARCH 6 ' FOR SECOND.

(b) SOLVING BOTH EQUATIONS SIMULTANEOUSLY 702 - 0.318 X = 1642 - 0.718 X

OR 0.718 X - 0.318 X = 1642 - 702

OR 0.363 X = 940 OR X = 940 / 0.363 = 2589.53 ~ 2590

HENCE TWO ESTIMATES AGREE IN   YEAR 2590

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