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A store finds that its sales decline after the end of an advertising campaign. On the day that the campaign ends, daily sales are $8,500 and 3 days after the end of the campaign daily sales are $5,100. Usual daily sales for the store total $3,500. Assume the decline in sales follows the pattern of Newton's Law of Cooling (Heating). What are daily sales for the store 7 days after the end of the advertising campaign

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Answer:

The sales for the store 7 days after the end of the advertising campaign is


G_7 =$3849.74

Explanation:

From the question we are told that

The daily sales on the end of campaign day is
G_o = $8,500

The daily sales three days after end of campaign day is
G_3 = $ 5,100

The usual day sales of the store is
G_u = $ 3,500

Generally the Newton's Law of Cooling (Heating). equation is mathematically represented as


G_t = G_u+ [(G_o -S_u ) * e^(-(k*t))]

Here t is the number of day after the campaign ended

Now substituting values to obtain the constant k

For t = 3


G_3 = G_u + [(G_o -S_u ) * e^(-(k*3))]


5100 = 3500 [(8500 -3500 ) * e^(-(k*3))]


e^(-(k*3)) = 0.32

=>
-3k = ln (0.6)

=>
-3k = -1.1394

=>
k = 0.380

So at t = 7


G_7 = G_u + [(G_o -S_u )] * e^(-(k*7))

substituting values


G_7 = 3500 + [(8500 -3500 )] * e^(-(0.3780*7))


G_7 =$3849.74

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