maths --plse help me..

posted by .

A bacteria culture has an initial population of 600. After 4 hours the population has grown to 1200. Assuming the culture grows at a rate proportional to the size of the population, find the function representing the population size after t hours and determine the size of the population after 8 hours.

  • maths --plse help me.. -

    amount = a e^(kt) where a is the initial value, k is a constant, and t is in hours

    1200 = 600 e^(k(4)
    2 = e^(4k)
    4k = ln 2
    k = ln2 /4

    amount = 600 e^((ln2/4)t)

    when t=8
    amount = 600 e^(2ln2)
    = 2400

    well, duh
    Since the doubling period seems to be 4 hours
    in 8 hours they would have doubled twice
    600 --> 1200 --> 2400

Respond to this Question

First Name
School Subject
Your Answer

Similar Questions

  1. math

    A bacteria culture starts with 260 bacteria and grows at a rate proportional to its size. After 4 hours there will be 1040 bacteria. (a) Express the population after t hours as a function of t. this is what i put as my answer but i …
  2. 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 exponential …
  3. Calculus AB

    The rate of growth dP/dt of a population of bacteria is proportional to the square root of t, where p is the population size and t is the time in days (0<equal t <equal 10). That is, dp/dt = ksqrt(t). The initial size of the …

    a bacteria culture grows with a constant per capita growth rate. After 2 hours there are 500 bacteria and after 6 hours the count is 312500, find the initial population and the population after 8 hours
  5. Calculus

    A bacteria culture contains 200 cells initially and grows at a rate proportional to its size. After half an hour the population has increased to 360 cells. (a) Find the number of bacteria after t hours. (b) Find the number of bacteria …
  6. calculus

    The count in a bacteria culture was 600 after 10 minutes and 1100 after 30 minutes. What was the initial size of the culture?
  7. Calculus (math)

    A bacteria culture grows with constant relative growth rate. The bacteria count was 784 after 2 hours and 117649 after 6 hours. What is the relative growth rate?
  8. Urgent math

    population growth model. Can anybody please help me out in trying to solve this problem?
  9. Urgent math

    The initial size of a culture of bacteria is 1000. After one hour the bacteria count is 4000. (a) Find a function n(t) = n0ert that models the population after t hours. n(t) = b)Find the population after 1.5 hours. (Round your answer …
  10. calculus

    The population of a culture of bacteria, P(t), where t is time in days, is growing at a rate that is proportional to the population itself and the growth rate is 0.3. The initial population is 40. (1) What is the population after 30 …

More Similar Questions