Calculus 2

A culture of bacteria is growing at the rate of 20e^0.8t cells per day, where t is the number of days since the culture was started. Suppose that the culture began with 50 cells.
(a) Find a formula for the total number of cells in the culture after t days.
(b) If the culture is to be stopped when the population reaches 700, when will this occur? (Round your answer to one decimal place.)

  1. 👍
  2. 👎
  3. 👁
  1. If N is the number of bacteria

    dN/dt = 20e^.8t
    N = 25 e^.8t + 50

    when N = 700
    700 = 25 e^.8t + 50
    e^.8t = 26
    take ln of both sides
    .8t = ln 26
    t = appr 4.07

    check:
    if t = 4.07
    N = 25 e^.8(4.07) + 50
    = 698.6 , not bad

    1. 👍
    2. 👎

Respond to this Question

First Name

Your Response

Similar Questions

  1. Calc

    The number of bacteria in a culture is increasing according to the law of exponential growth. There are 125 bacteria in the culture after 2 hours and 350 bacteria after 4 hours. a) Find the initial population. b) Write an

  2. Math

    A culture of bacteria in a petri dish is doubling every hour. If there are 100 bacteria at time t=0, how many bacteria will there be in 12 hours?

  3. Steve - Stat

    A Bacteria has a doubling period of 8 days. If there are 2250 bacteria present now, how many will there be in 33 days? find the growth rate (Round this to 4 decimal places). Growth Rate___________. There will be _________

  4. Chem

    suppose that you place exactly 100 bacteria into a flask containing nutrients for the bacteria and that you find the following data at 37 °C: t (min):0 15.0 30.0 45.0 60.0 Number of bacteria: 100 200 400 800 1600 What is the

  1. Math

    a lab has two bacterial cultures. culture a contains 8×10^4 bacteria and culture B contains 4 × 10^6 bacteria. How do the two cultures compare in size?

  2. math

    A biologist grows a culture of bacteria as part of an experiment. At the start of the experiment, there are 75 bacteria in the culture. The biologist observes that the population of bacteria dobules evert 18 minutes. Which of the

  3. Math

    Bacteria can multiply at an alarming rate when each bacteria splits into two new cells, thus doubling. If we start with only bacteria which can double every hour, how many bacteria will we have by the end of the day?

  4. math

    A lab is growing bacteria in a culture dish. The amount of bacteria in the dish doubles every 3 hours. Initially, there are 500 bacteria in the dish. How many are in the dish after 9 hours? My answer: 4000 -(5)^-1 My answer: -1/5

  1. math

    The rate of increase of bacteria in a culture is proportional to the number of bacteria present .if the original number of bacteria double in the two hours, in how many hours will it be five times?

  2. Algebra 1

    I am having trouble with a few questions....Wondering if you could help...My answers have the *** by them..... 1. A lab is growing bacteria in a culture dish. The amount of bacteria in the dish doubles every 3 hours. Initially,

  3. Algebra 2

    If there are initially 1500 bacteria in a culture, and the number of bacteria double each hour, the number of bacteria after t hours can be found using the formula N=1500(2^t). How many bacteria will present after 7 hours? I think

  4. SCIENTIFIC NOTATION

    A lab has two bacteria cultures. Culture A contains 8*10^4 bacteria and culture B contains 4*10^6 bacteria. How do the two cultures compare in size? A. Culture A contains twice as many bacteria as Culture B B. Culture A contains

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