Exponents-word problem

posted by .

A culture starts at 8600 bacteria. After one hour the count is 10,000.
Find a function that models the number of bacteria n(t) after t hours.

The answer is n(t) = 8600e^.1506t

Where does this 0.1506 come from?

Thanks.

n(t) = 8600 e^(kt), where k is an unknown constant and t is the number of hours. We know that n(1), or the population after one hour is 10000. So 10000 = 8600e^(k*1)
10000/8600 = e^k
natural log ln(10000/8600) = k = .1508

The general expression is n(t) = no* e^(t/T), where T is the time for an increase by a factor of e.
In this case,
10000 = 8600 e^(1/T)
That equation can be solved for T.
10000/8600 = 1.16279 = e^(1/T)
Take the natural log of both sides.
0.15082 = 1/T
n(t) = e^(0.15082 t)
The 0.1506 in your version is not quite right.

Respond to this Question

First Name
School Subject
Your Answer

Similar Questions

  1. 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)=____________?
  2. 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) …
  3. 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 …
  4. 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 …
  5. 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?
  6. Math

    A culture contains 12,000 bacteria. After an hour the count is 25,000. Find the number of bacteria after 3 hours.
  7. Urgent math

    population growth model. Can anybody please help me out in trying to solve this problem?
  8. 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 …
  9. math

    A culture starts with 8300 bacteria. After one hour the count is 10,000. (a) Find a function that models the number of bacteria n(t) after t hours. (Round your r value to three decimal places.)
  10. PreCalc

    The initial size of a culture of bacteria is 1500. After 1 hour the bacteria count is 12000. (a) Find a function n(t) = n0e^rt that models the population after t hours. (Round your r value to five decimal places.) n(t) = (b) Find the …

More Similar Questions