Sales Decay At the end of an advertising campaign weekly sal

Sales Decay At the end of an advertising campaign, weekly sales declined according to the equation y = 8,000(3^-0.05x) dollars, where x is the number of weeks after the campaign ended. Determine the sales at the end of the ad campaign. (at x = 0) Determine the sales 6 weeks after the end of the campaign. How do we know, by inspecting the equation that this function is decreasing? According to this model, will the sales ever fall to zero?

Solution

y = 8000(3^-0.05x)

a) x = 0 ; y = 8000*1 = 8000 sales at the end of campaign

b) After x = 6 weeks:

y = 8000(3^-0.05*6) = 5753.78 dollars

c) The function is deceasing because the exponent is -ve i.e. -0.05

d) Sales will zero : x>>>0 ; y ----> 0

for x = 250 ;y = 0.009 = 0 ( approx.)