National ad spending in newspapers was $5.3 billion in 2009, and the spending ha

Question

National ad spending in newspapers was $5.3 billion in 2009, and the spending has decreased by $0.42 billion per year. Online ad spending at newspaper websites was $3.1 billion in 2009, and the spending has increased by $0.32 billion per year (Source: Newspaper Association of America). a. Let N(t) and I(t) be the spending (in billions of dollars) for national newspaper ads and online newspaper ads, respectively, both at t years since 2009. Find equations of N and I. b. Predict when ad spendings for national newspaper ads and for online newspaper ads will be equal. What will that spending be? c. Solve the inequality N(t) > I(t). What does your result mean in this situation?

Explanation / Answer

a) N(t) = 5.3 - 0.42t

I(t) = 3.1 - 0.32t

b) N(t) = I(t)

5.3 - 0.42t = 3.1 - 0.32t

2.2 = 0.1t

t = 22

So, in 2009 + 22 = 2029 they will be equal.

c) N(t) > I(t)

5.3 - 0.42t > 3.1 - 0.32t

2.2 > 0.1t

or

0.1t < 2.2

t < 22

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