Question

An advertising company designs a campaign to introduce a new product to a metropolitan area of population 5 Million people. Let P(t) denote the number of people (in millions) who become aware of the product by time t. Suppose that P increases at a rate proportional to the number of people still unaware of the product. The company determines that no one was aware of the product at the beginning of the campaign, and that 50% of the people were aware of the product after 20 days of advertising. The number of people who become aware of the product at time t is:

Answer 1

The number of people who became aware at the time T = 20 days = 2.5 million

Explanation:

p(t) = 5 million

To = 0

T1 = 20 days

P(T1 ) = 50% * 5 = 2.5 million

hence to confirm the value of t where t = 20

P(T1) =
`6 - 4 ((4)/(5) )^{(1)/(50)t }`

=
`6 - 4 ((4)/(5) )^(0.4)`

= 6 - 4(0.9146)

p(20 ) ≈ 2.5 million