A national fast food company has just analyzed the effect of the latest sales promotion.

Question

A national fast-food company has just analyzed the effect of the latest sales promotion.It has determined that the sales decay for its milkshakes is given by , where  is the weekly sales and  is the number of weeks that have passes since the end of the sales promotion.

a) Determine the sales 4 weeks after the end of the promotion:

Round answer to 2 decimal places.

Sales = $ 

b) If no new campaign is started, how many weeks after the end of the promotion will sales drop below 30,000?

Round answer to 1 decimal place.

Num. weeks = 

Answer 1

You are told that S (the weekly sales) = 360000e^-0.6x where x is the number of weeks gone by. So, to determine the sales after 4 weeks, just plug in x = 4 into the equation.

S = 360000e^-0.6x

S = 360000e^-0.6(4)

S = 360000e^-2.4

S = S = 360000(0.0907179533)

S = $32,658.46

To find the number of weeks that has gone by when the sales drop below $30,000, plug in 30,000 as the sales and solve for "x":

S = 360000e^-0.6x

30000 = 360000e^-0.6x

30000/360000 = e^-0.6x

0.08333333 = e^-0.6x

ln(0.08333333) = ln(e^-0.6x)

-2.48490665 = -0.6x•ln(e)

-2.48490665 = -0.6x

x = -2.48490665/-0.6

x = 4.1415

In rounding, round up because you are trying to find the number of weeks gone by such that the sales is below $30,000 and if you round to 4.1 weeks, the sales would be slightly above $30,000. So x = 4.2 weeks