Pre-Calculus

posted by .

A culture of bacteria obeys the law of unlimited growth. If 500 bacteria are present initially and there are 800 after 1 hour, how many will be present in the cultrue after 5 hours? How long until there are 20,000 bacteria?


Hmmm, what is "the law of unlimited growth"? In any case, this looks like exponential growth to me.
The most basic formula for exponential growth is
A = P*er*t where r is the rate of growth, t is the time, P is the initial amount and A is observed growth.
Here 800 = 500*er*1hr so
ln(1.6units) = r*1hr or ln(1.6units)/1hr = r or
A = 500*(1.6)t
Substitute 5 for t to answer the first question, i.e.
A = 500*(1.6)5
To answer the second part set A=20,000
20,000=500*(1.6)t or
40 = (1.6)t
It looks to be slightly less than 8 hrs. You can verify this.

Respond to this Question

First Name
School Subject
Your Answer

Similar Questions

  1. Pre-Calculus

    The population of a particular type of bacteria doubles in number every 12 hours. a)if there are 8 bcteria initially, write an equation that models the number of bacteria present after x 12 hours. b)How many bacteria will be present …
  2. Precalculus

    NEED HELP ASAP PLEASE!! A bacteria culture starts with 2000 bacteria and the population doubles every 3 hours. a) A function that models the number of bacteria after t hours is p(t)=____________?
  3. precalculus

    A bacteria culture initially contains 1500 bacteria and doubles every half hour. a) Find an expression for the number of bacteria after t hours. Q(t)= b) The number of bacteria after 20 minutes is (the answer must be an integer) c) …
  4. pre calculus

    if there are initial 2500 bacteria in a culture, and the number of bacteria double each hour, the number of bacteria after t hours cab n be found using the formula=N=2500(2^t).how long will it take the culture to grow to 75,000 bacteria.
  5. 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 …
  6. MATH :)

    3. In Biology, it is found that the bacteria in a certain culture double every half-hour. If the initial number of bacteria in culture is 1000, A. Find the defining equation for the number N of bacteria in culture after T hours, assuming …
  7. 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?
  8. Calculus

    A colony of bacteria is grown under ideal conditions in a laboratory so that the population increases exponentially with time. At the end of 2 hours, there are 4,800 bacteria. At the end of 4 hours, there are 19,00 bacteria. How many …
  9. Math

    Salmonella bacteria grows rapidly in a nice warm place. If just a few hundred were left on a cutting board when a chicken was cut up, and they get into the potato salad, the population begins compounding. Suppose the number present …
  10. College Algebra

    The number of bacteria in a certain culture increased from 500 to 1000 between 7:00 A.M. and 9:00 A.M. Assuming growth is exponential, the number f(t) of bacteria t hours after 7:00 A.M. is given by f(t) = 500(2)^t/2. (a) Estimate …

More Similar Questions