# 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...

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 days will elapse before 450 students have heard the rumor?

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The number of people that hear a rumor in a college is modeled by N = P*(1 - e^(-0.15*d)) where P is the total number of students and d is the number of days that pass.

If the total number of students is 1000 and 450 people have to hear the rumor, the number of days that pass after which this happens is give by:

450 = 1000*(1 - e^(-0.15*d))

=> 1 - e^(-0.15*d) = 450/1000

=> e^(-0.15*d) = 1 - 450/1000

=> e^(-0.15*d) = 550/1000

Take the natural log of both the sides

= -0.15*d = ln(.55)

d = 3.98 days

The number of days after which 450 students hear the rumor is 3.98 or approximately 4 days.
The text passage provides a mathematical model for the spread of a rumor in a college community and then poses a specific question about how many days it will take for 450 students to hear the rumor in a community of 1000 students. The passage also includes a detailed solution to this question.
single_question_with_answer
Given a text passage, determine:
    1. If it contains a mathematical question (including word problems or calculations)
    2. If an answer to that mathematical question is provided in the text

First, describe the content structure you found in 1-2 sentences.

Then provide your analysis in the following format:
TYPE: <one of the following values>
- NO_QUESTION
- SINGLE_QUESTION
- SINGLE_QUESTION_WITH_ANSWER
- MULTIPLE_QUESTIONS
- MULTIPLE_QUESTIONS_WITH_ANSWERS
system
# 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...

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 days will elapse before 450 students have heard the rumor?

Posted on

The number of people that hear a rumor in a college is modeled by N = P*(1 - e^(-0.15*d)) where P is the total number of students and d is the number of days that pass.

If the total number of students is 1000 and 450 people have to hear the rumor, the number of days that pass after which this happens is give by:

450 = 1000*(1 - e^(-0.15*d))

=> 1 - e^(-0.15*d) = 450/1000

=> e^(-0.15*d) = 1 - 450/1000

=> e^(-0.15*d) = 550/1000

Take the natural log of both the sides

= -0.15*d = ln(.55)

d = 3.98 days

The number of days after which 450 students hear the rumor is 3.98 or approximately 4 days.
user
The text passage provides a mathematical model for the spread of a rumor in a college community and then poses a specific question about how many days it will take for 450 students to hear the rumor in a community of 1000 students. The passage also includes a detailed solution to this question.

TYPE: SINGLE_QUESTION_WITH_ANSWER