Marketing—Advertising Budget: The number of dollars spent on advertising for a product influences the number of items of the product that will be purchased by customers. The number of Krypto-Cases sold for a new smartphone is a function of the amount of advertising spent and can be modeled by
where x represents the amount spent on advertising, measured in thousands of dollars, and N(x) represents the number of cases purchased. 520
(a) Given
, evaluate N(20) and N′(20) and interpret each.
(b) Evaluate N(36) and N′(36), and interpret each.
(c) As the amount of dollars, x, spent on advertising increases, what happens to N′(x), the rate of change in the items sold per thousands in advertising dollars spent? Is it increasing or decreasing?
(d) Graph N and N′, and use the graphs to graphically verify your answer for part (c).
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