(question 3.2 : 2e part B) the number n(t) of people in a community who are expo

Question

(question 3.2 : 2e part B)
the number n(t) of people in a community who are exposed to a particular advertisement is governed by the logistic equation ( where t is measured in days). Initially, N(0)=500, and is observed that N(1)=1000.

(a) 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.

Answer for part A is : N(t)= 50236/(1 + 99.5e^(-0.7033t))

Question part B: Using N(t) found in part a, estimate how long it will take for 49,000 people to see the advertisement.

Explanation / Answer

N(t) = 49000 , t = ?

50236/(1 + 99.5e^(-0.7033t)) = 49000

(1 + 99.5e^(-0.7033t)) = 50236/49000

99.5e^(-0.7033t) = 50236/49000 - 1 = 0.0252

e^(-0.7033t) = 0.0252/99.5 = 0.0002535

-0.7033t = ln(0.0002535)

t = ln(0.0002535)/(-0.7033) 11.7733

Thus it takes almost 11 days and 19 hours.

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