A new school has opened in the area the school did not have yearbook before 2010. In 2010 there were 500 yearbooks sold. In 2014 there were 1000 yearbooks sold. Write the linear function that represents the number of yearbooks sold per year

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Mathematics

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10 March, 13:12

A new school has opened in the area the school did not have yearbook before 2010. In 2010 there were 500 yearbooks sold. In 2014 there were 1000 yearbooks sold. Write the linear function that represents the number of yearbooks sold per year

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Reece Cowan · Answer 1

Step-by-step explanation:

The increase in the number of books sold each year follows an arithmetic progression, hence it is linear.

The formula for the nth term of an arithmetic progression is expressed as

Tn = a + (n - 1) d

Where

Tn is the nth term of the arithmetic sequence

a is the first term of the arithmetic sequence

n is the number of terms in the arithmetic sequence.

d is the common difference between consecutive terms in the arithmetic sequence.

From the information given,

a = 500 (number of books in the first year.

T5 = 1000 (the number of books at 2014 is)

n = 5 (number of terms from 2010 to 2014). Therefore

T5 = 1000 = 500 + (5 - 1) d

1000 = 500 + 4d

4d = 500

d = 500/4 = 125

The linear function that represents the number of yearbooks sold per year will be

T (n) = 500 + 125 (n - 1)