Question

An advertising campaign has a target audience 100,000 individuals. At the beginning of the campaign, none of the individuals in this group are aware of the product. After 1 week of the campaign, 10,000 individuals in the target group have heard of the product. Assume that the rate at which members of the target group become aware of the product is proportional to the number in the group who have not heard of the product.

(a) Set up a differential equation involving A and A' (where A'=(dA/dt).
(b) Find an expression for A(t).

Answer 1

Would it be a logistic model?

Answer 2

like y'=ky(M-y)

Answer 3

Typically a logistic model has a min or max does it not?

Answer 4

not really

Answer 5

So if I'm understanding this correctly, once solved, the Answer would be an exponential with A=10,000; (if I remember my diff. eq correctly)

Answer 6

The example I am looking at breaks down to y=M/(1+Ce^(kt))

Answer 7

A(0)=0
A(1)=10,000

Answer 8

That's what I was aiming for; sorry, I don't really use logistic diff. eq in physics. mostly second order diff. eq.

Answer 9

Thinking A(t)=M/(1+Ce^(kt))

Yea its all in the word problem, just trying to extract it and put it in to place correctly. Once I figure that out the math is easy, lol.

Answer 10

0=100000/1+C
C=100000

10000=100000/1+Ce(k)
???

Answer 11

I can probably send you my old Diff eq. text on logistics if you want. sry wasn't much help

Answer 12

it's a pdf and I THINK OS allows posting of smaller pdf's

Answer 13

Ok, I've got like 30 pdf files, was logistics first order or second order diff. eq?

Answer 14

First Order but I am also doing second order so if you can send those also would be appreciated.