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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

Answer :

okpalawalter8

Answer:

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

          [tex]G_7 =[/tex]$3849.74

Step-by-step explanation:

From the question we are told that

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

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

     The  usual day sales of the store is [tex]G_u[/tex]  =  $ 3,500

     

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

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

Here t is the number of day after the campaign ended

Now substituting values to obtain the constant k

For  t =  3

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

          [tex]5100 = 3500 [(8500 -3500 ) * e^{-(k*3)}][/tex]

         [tex]e^{-(k*3)} = 0.32[/tex]

=>     [tex]-3k = ln (0.6)[/tex]

=>      [tex]-3k = -1.1394[/tex]

=>        [tex]k = 0.380[/tex]

So at  t =  7

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

substituting values

    [tex]G_7 = 3500 + [(8500 -3500 )] * e^{-(0.3780*7)}[/tex]

    [tex]G_7 =[/tex]$3849.74

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