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) = 500, and it is observed that n(1) = 1000. solve for n(t) if it is predicted that the limiting number of people in the community who will see the advertisement is 50,000.

Step-by-step explanation:

The logistic equation is

where:

c/(1+a) is the initial value.

c is the limiting value

r is constant determined by growth rate

So we are given that:

N(0)=500 or that c/(1+a)=500

If your not sure about his initial value of c/(1+a) then replace x with 0 in the function N:

Simplify:

Anyways we are given:

.

Cross multiplying gives you .

We are also giving that N(1)=1000 so plug this in:

Simplify:

So this means

Cross multiplying gives you

We are giving that c=50000 so we have these two equations to solve:

and

I'm going to solve first because there is only one constant variable here,.

Divide both sides by 500:

Subtract 1 on both sides:

Now since we have we can find in the second equation:

with

Divide both sides by 1000

Subtract 1 on both sides:

Divide both sides by 99:

Take natural log of both sides:

Multiply both sides by -1:

So the function N with all the write values plugged into the constant variables is: