Question

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 1

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