Calculus

The rate of growth dP/ dt of a population of bacteria is proportional to the square root of t with a constant coefficient of 9, where P is the population size and t is the time in days (0¡Üt¡Ü10). The initial size of the population is 700. Approximate the population after 7 days. Round the answer to the nearest integer.

  1. 👍
  2. 👎
  3. 👁
  1. dP/dt = 9√t
    P(t) = 6t^(3/2)+c
    P(0) = 700, so c=700 and thus

    P(t) = 6t^(3/2)+700

    as you can see, this function models some slow growth. You sure dP/dt is not proportional to P?

    1. 👍
    2. 👎

Respond to this Question

First Name

Your Response

Similar Questions

  1. Algebra II Help

    4) The function f(x)=2(3)^x represents the growth of a dragonfly population every year in a remote swamp. Rose wants to manipulate the formula to an equivalent form that calculates seven times a year, not just once a year. Which

  2. Math

    A certain type of bacteria is growing at an exponential rate that can be modeled by the equation y=ae^kt, where t represents the number of hours. There are 300 bacteria initially, and 1500 bacteria 5 hours later. Find the rate of

  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

  4. Honors Algebra

    A biologist is researching a newly discovered species of bacteria. At time t=0 hours, she puts on hundred bacteria into a Petri dish. Six hours later, she measures 450 bacteria. Assuming exponential growth, what is the growth rate

  1. Algebra 2 check my answer please?

    The population of a bacteria in a Petri dish doubles every 16 hours. The population of the bacteria is initially 500 organisms. How long will it take for the population of the bacteria to reach 800? Round your answer to the

  2. 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:

  3. 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

  4. 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

  1. math

    the small intestine bacteriaa, while inhabiting areas optimal for growth have a doubling time of roughly 10 hours. A normal small intestine starting population would be approximately 10,000 bacteria per ml of fluid a) write an

  2. 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

  3. Math - Derivative of a polynomial function

    The population, p in thousands of bacteria colony can be modelled by the function p(t)=200+20t-t^2, where t is the time, in hours, t is greater than or equal to zero. a) Determine the growth rate of the bacteria population at each

  4. AP CALC

    At any time t=>0 , in days, the rate of growth of a bacteria population is given by y' = ky, where y is the number of bacteria present and k is a constant. The initial population is 1500 and the population quadrupled during the

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