A cereal company finds that the number of people who will buy one of its product

Question

A cereal company finds that the number of people who will buy one of its products in the first month that it is introduced is linearly related to the amount of money it spends on advertising. If it spends $40,000 on advertising, then 100,000 boxes of cereal will be sold, and if it spends $60,000, then 200,000 boxes will be sold. a) Write a formula to express the amount spent on advertising as a linear function of the number of cereal boxes sold. Be sure to specify what your variables represent (my teacher picked n for number of cereal boxes sold and A for amount spent on advertising). Show work. b) What is the initial value of this function and what does it represent.

Explanation / Answer

a)

Let

A =amount spent on advertising

n= number of cereal boxes sold

Find the equation of line through (100000,40000) and ( 200000,60000)

Slope =(60000 -40000)/ (200000 -100000) = 1/5

Thus, using point slope form,

A-40000 = (1/5) (n -100000 )

A-40000 = (1/5) n -20000

A= (1/5) n +20000

==================

b)

Substitute 0 for n to obtain

A= (1/5) *0 +20000

=20000

Thus, initial value is 20000.

It represnts the amount spent is $20000, before selling the product.

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