Suppose that the number of bacteria in a certain population increases according to a continuous exponential growth model. A sample of 1800 bacteria selected from this population reached the size of 2272 bacteria in five hours. Find the hourly growth parameter.

  1. 👍 0
  2. 👎 0
  3. 👁 988
  1. so
    number = a e^(kt)

    2272 = 1800 e^(5k)
    1.26222... = e^5k
    ln 1.26222... = 5k
    k = .04657.. <----- your hourly growth parameter

    the instantaneous rate of growth is appr 4.657% per hour.

    1. 👍 0
    2. 👎 0

Respond to this Question

First Name

Your Response

Similar Questions

  1. 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

  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

  3. Geometry

    Suppose you are studying bacteria in biology class the table shows the number of bacteria after n doubling periods n(periods)[0 1 2 3 4 5] billions of bacteria [3 6 12 24 48 96] your teacher asks you to predict the number of

  4. Calculus

    Explain, using the theorems, why the function is continuous at every number in its domain. F(x)= 2x^2-x-3 / x^2 +9 A) F(x) is a polynomial, so it is continuous at every number in its domain. B) F(x) is a rational function, so it

  1. Algebra

    The number of bacteria in a certain population increases according to a continuous exponential growth model, with a growth rate parameter of 3.7% per hour. How many hours does it take for the size of the sample to double? Note:

  2. Calculus

    A bacteria population is 3000 at time t = 0 and its rate of growth is 1000 ยท 6t bacteria per hour after t hours. What is the population after one hour? (Round your answer to the nearest whole number.)

  3. Algebra

    The exponential function f(x) = 3(5)x grows by a factor of 25 between x = 1 and x = 3. What factor does it grow by between x = 5 and x = 7? A) 5 B) 25 C) 125 D) 625 3) If a city that currently has a population of 1000 triples in

  4. Calculus

    Suppose that a population of bacteria triples every hour and starts with 700 bacteria. (a) Find an expression for the number n of bacteria after t hours. n(t) = ? (b) Estimate the rate of growth of the bacteria population after

  1. 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

  2. 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

  3. math

    the population of a southern city follows the exponential law. If the population doubled in size over an 18 month period and the current population in 10000, what will be the population 2 years from now? the equation for the

  4. Algebra

    Two different businesses model their profits over 15 years, where x is the year, f(x) is the profits of a garden shop, and g(x) is the profits of a construction materials business. Use the data to determine which function is

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