Problema Solution
A company is trying to expose as many people as possible to a new product through television advertising in a large metropolitan area with 2 million possible viewers. A model for the number of people N, in millions, who are aware of the product after t days of advertising was found to be:
N=2(1-e^-0.037t)
How many days, to the nearest day, will the advertising campaign have to last so that 80% of the possible viewers will be aware of the product?
Answer provided by our tutors
80% of the 2 million possible viewers is
0.80*2*10^6 = 1.6*10^6
we need to find t so that N = 1.6 that is
2(1-e^-0.037t) = 1.6 divide both sides by 2
1-e^-0.037t = 0.8
e^-0.037t = 1 - 0.8
e^-0.037t = 0.2
ln (e^-0.037t) = ln 0.2
-0.037t = ln 0.2
t = - (ln2/0.037)
t = - (-1.6094379124/0.037)
t = 43.498 days or 43
t = 43 days
the advertising campaign has to last more then 43 days.