Calculus I, differentiation

The number, N, of people who have heard a rumor spread by mass media by time, t, is given by N(t)=a(1−e−kt). There are 6 million people in the population, who hear the rumor eventually. If 5% of them heard it on the first day, find the percentage of the population who have heard the rumor after 5 days.

I found N'(t)=(ae^-(bx))+axe^-(bx)
and i figure a=6M*.05=300000, but i cannot find the %population after 5 days. any help would be awesome, Thanks in advance!

  1. 👍
  2. 👎
  3. 👁
  1. N(t) = a(1 - e^-kt)
    After 1 day, t=1, and we have

    .05a = (1 - e^-k)
    .05 = 1 - e^-k
    0.95 = e^-k
    k = -ln 0.95 = 0.0513
    N(t) = a(1 - e^-0.0513t)

    So, by the end of day 5,

    N(5) = a(1 - e^-.2565) = .226a = 22.6%

    have heard the rumor

    1. 👍
    2. 👎

Respond to this Question

First Name

Your Response

Similar Questions

  1. EdTech

    1) what is an example of bias in media A. A website that presents a controversial opinion as though it were fact. B. A television news program that presents both sides of a particular issue**** C. A podcast expressing an authors

  2. english

    Select the excerpt from "Mother Tongue" by Amy Tan that best describes language bias. 1. I've heard other terms used, "limited English," for example. But they seem just as bad, as if everything is limited, including people's

  3. Precal

    The number of people in a town of 10,000 who have heard a rumor started by a small group of people is given by the following function: N(t) = 10,000/(5 + 1245e-.97t) 14. How many people were in the group that started the rumor?

  4. calculus

    The number, N, of people who have heard a rumor spread by mass media at time, t , is given by N(t) = a(1 - e^(kt)) There are 250000 people in the population who hear the rumor eventually. 25 percent of them heard it on the first

  1. geography

    Which of the following is an example of an environmental challenge in Africa today? A. conflict between the Hausa people and the Yoruba people in Nigeria B. the lack of machinery needed for manufacturing C. a limited number

  2. Calculus

    During a certain epidemic, the number of people that are infected at any time increases at rate proportional to the number of people that are infected at that time. 1,000 people are infected when the epidemic is first discovered,

  3. Math

    In a community of 800 people the rate at which a rumor spreads is jointly proportional to the number of people who have heard the rumor and the number of people who have not heard it. Given that the rumor is spreading at the rate

  4. SAT essay

    Please scores my essay Thanks so much!!! Assignment: Do newspapers, magazines, television, radio, movies, the Internet, and other media determine what is important to most people? In modern society, people gain most of their

  1. Algebra

    A scientist wants to research the potential spread of germs by contact. She knows that the number of possible handshakes within a group of n people is given by the equation N=1/2(n^2-n). Everyone at a party shook hands. There were

  2. Social Studies

    After the Buddha's death, how did Buddhism spread? A. Missionaries traveled around Asia and taught people about Buddhism. B. Asian governments heard about the Buddha and required people to become Buddhists. C. Doctors throughout

  3. Life Skills

    6. Carlos loves to spend time with his younger brother. Even though he is busy with school and work, Carlos always makes time for them to do things together what is this an example of? a. honesty b. justice c. priorities *** d.

  4. Health

    Identifying Values Quiz: 1. Your values come from many different sources. Which is one source that can influence your values? Cooperation Ability Media *** Choices 2. Ellie believes it is important to exercise and eat a healthy

You can view more similar questions or ask a new question.