Q. 106 - Precalculus Enhanced with Graphing Utilities

Question

Spreading of Rumors A model for the number N of people in a college community who have heard a certain rumor is

             $N=P(1-e^{-0.15d})$

where P is the total population of the community and d is the number of days that have elapsed since the rumor began. In a community of 1000 students, how many students will have heard the rumor after 3 days? 

Step-by-Step Solution

Answer

In a community of 1000 students, approx $362$ students will have heard the rumor after 3 days

Step 1.Given information

Let us consider the total population be .
And the number of people who heard the rumor be 
Then $N=P(1-e^{-0.15d})$

Step 2.Finding how many students will have heard the rumor after 3 days?

Let the number of days be 3 the total population be 1000
Then we get

 $$\begin{gathered} N=P(1-e^{-0.15d}) \\ =1000(1-e^{-0.15\times 3}) \\ =362.3718484 \\ \approx 362 \end{gathered}$$