Answer to Question #151086 in Calculus for Angelo

Question #151086

A company has learned that when it initiates a new sales campaign, the number of sales per

day increases. However, the number of extra daily sales per day decreases as the impact of the campaign wears off. For a specific campaign the company has determined that if there are e 𝑆(𝑑) extra daily sales as a result of the campaign and 𝑑 days have elapsed since the campaign ended, then 𝑆(𝑑) = 1000 (3^βˆ’π‘‘/2). Find the rate at which the extra daily sales are decreasing when (a) 𝑑 = 4 and (b) 𝑑 = 10.


1
Expert's answer
2020-12-20T17:56:39-0500

"S'(t) = 1000 \\times -\\frac{1}{2} 3^{-\\frac{t}{2}} \\ln{3} = -500\\ln{3}\\left(3^{-\\frac{t}{2}}\\right)\\\\\n\n\nS'(4) = -500\\ln{3}\\left(3^{-\\frac{4}{2}}\\right) = -61.03\\\\\n\nS'(10) = -500\\ln{3}\\left(3^{-\\frac{10}{2}}\\right) = -2.26\\\\\n\n\\textsf{Therefore, the rate at which the}\\\\\n\\textsf{extra daily sales are decreasing}\\\\\n\\textsf{when}\\\\\n\n(a) t = 4\\,\\,\\textsf{is}\\,\\, 61.03\\,\\, \\textsf{Sales}\/\\textsf{day.}\\\\ \n\n(b) t = 10\\,\\,\\textsf{is}\\,\\, 2.26\\,\\,\\textsf{Sales}\/\\textsf{day.}\\\\"


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