Question

If the growth rate of bacteria in a culture medium is directly proportional to the difference between the number of bacteria and a certain optimal number N¯, derive an expression for the number of bacteria n as a function of the time t given that the initial number of bacteria placed in the culture mediam is N0 and that the constant of proportionality is λ. Sketch, by inspection, the graph of n = n(t). How long does it take for the difference in the number of bacteria and the optimal number to reduce to 1 4 of the initial difference?

please could you assist on how to set up the model

Answer #1

The temperature T of a body will increase or decrease at a rate
proportional to the temperature difference respectively below or
above the surrounding temperature, T¯, the constant of
proportionality being k. Derive an expression depicting the
temperature of the body as a function of the time given that its
initial temperature is T0. Sketch, by inspection, the
graph of T = T(t) when T0 < T¯, and when
T0 > T¯.

In a certain culture where the rate of growth is proportional to
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7 days there are 10 million bacteria present in the culture how
many were present initially?

The population of a bacteria in a culture grows at a rate
proportional to the number of bacteria present at time t. After 3
hours it is observed that 400 bacteria are present. After 10 hours
2000 bacteria are present. What was the initial number of
bacteria?

A bacteria culture initially contains 40 cells and grows at a
rate proportional to its size.
After 2 hours the population has increased to 120.
a) Find an expression (in exact simplest form) for the number of
bacteria after t hours.
b) Find the rate of growth at t = 5 hours. Round your final answer
to nearest whole number.

The population of bacteria in a culture grows at a rate
proportional to the number of bacteria present at time t. After 2
hours from the beginning, it is observed that 500 bacteria are
present. After 5 hours (from the beginning), 1500 bacteria are
present. What is the initial number of bacteria P0 ?
Hint: Use P(t) = P0ekt
A - 240 at beggining
B - 198 at beggining
C - 541 at the beggining
D - None of the...

This exercise uses the population growth model.
The count in a culture of bacteria was 600 after 2 hours and 38,400
after 6 hours. Find a function that models the number of bacteria
n(t) after t hours. (Enter your answer
in the form
n0ert.
Round your
n0
value to the nearest whole number. Round your r value to two
decimal places.)

Bacteria grown in a certain culture
increase at a rate proportional to the amount present. If there are
3000 bacteria present initially and there are 5000 in 1 hour, how
many bacteria will there be in 3.5
hours?

The rate of growth of a certain cell culture is proportional to
its size. In 8 hours a population of 1 million cells grew to 9
million. How large will the cell culture be after 20 hours?

1) In a bacterial culture, the number of bacteria, f(t), is
defined by the equation f(t) = Be0.02t where B is a constant, and t
is the time elapsed in minutes the initial number of bacteria is
1000 . Note: initial number of bacteria means the number at the
start or t = 0 A. compute for the constant B B. determine the
number of bacteria after 50 minutes
2) In a certain bacterial culture the number of bacterial cells...

The rate of growth dP/dt of a population of bacteria is
proportional to the square root of t with a constant coefficient of
7, where P is the population size and t is the time in days
(0≤t≤10). The initial size of the population is 600. Approximate
the population after 7 days. Round the answer to the nearest
integer.

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