The number Nt of people in a community who are exposed to a

The number

N(t)

of people in a community who are exposed to a particular advertisement is governed by the logistic equation. Initially,

N(0) = 700,

and it is observed that

N(1) = 1400.

Solve for

N(t)

if it is predicted that the limiting number of people in the community who will see the advertisement is 70,000. (Round all coefficients to four decimal places.)

N(t) =   

Solution

The form of N(t) can be written as
.. N(t) = 70,000/(1+a*e^(-b*t))
where \"a\" and \"b\" are determined from the given conditions

N(0) = 70,000/(1+a) = 70000/(1+a) = 700 ====> a=99
N(1) = 70,000/(1+a*e^-b) = 70000/(1+99*e^-b), so
.. 1+99*e^-b = 50 ====> 99*e^-b = 49
.. b = -ln(49/99) 0.7033

N(t) = 70000/(1+99*e^(-0.7033t))