Question
In: Math
The population of bacteria (in millions) in a certain culture x hours after an experimental nutrient...
The population of bacteria (in millions) in a certain culture x hours after an experimental
nutrient is introduced into the culture is
P(x)=25x/6+x^2.
Use the differential to approximate the changes in population for the following changes in x.a.
2
to
2.5
b.
3
to 3.25
Solutions
milcah answered 2 years agoRelated Solutions
The population of a culture of bacteria is calculated and recorded after each hour, for a...
The population of a culture of bacteria is calculated and
recorded after each hour, for a six-hour period.
0
98
1
206
2
405
3
783
4
1550
5
2520
6
5630
Sketch a graph to illustrate these data.
Compare linear, quadratic, and exponential regression models.
List the equations and correlation coefficients for each type of
function. Provide a graph and include the regression lines.
Use each model to determine the initial number of bacteria at
the beginning of the...
USE PYTHON TO SOLVE THIS PROBLEM A bacteria culture grows exponentially. After 2 hours, the bacteria...
USE PYTHON TO SOLVE THIS PROBLEM
A bacteria culture grows exponentially. After 2 hours, the
bacteria count was 400 cells and after 6 hours, the bacteria count
was 20,000 cells.
a) Solve a system of equations to find (approximately) k and y0
(HINT: If will help to assume K is real in the symbols command)
b) Use this to determine when the bacteria count reaches
2,000,000 (exact and approximate).
c) Suppose 400 was the “initial” amount and 20,000 the count...
USE PYTHON TO SOLVE THIS PROBLEM A bacteria culture grows exponentially. After 2 hours, the bacteria...
USE PYTHON TO SOLVE THIS PROBLEM
A bacteria culture grows exponentially. After 2 hours, the
bacteria count was 400 cells and after 6 hours, the bacteria count
was 10,000 cells.
a) Solve a system of equations to find (approximately) k and y0
(HINT: If will help to assume K is real in the symbols command)
b) Use this to determine when the bacteria count reaches
1,000,000 (exact and approximate).
c) Suppose 400 was the “initial” amount and 10,000 the count...
Under ideal conditions a certain bacteria population is known to double every three hours. Suppose that...
Under ideal conditions a certain bacteria population is known to
double every three hours. Suppose that there are initially 100
bacteria.
(a) What is the population after 15 hours?
(b) What is the population after t hours?
(c) Find the population after 20 hours.
(d) Find the time at which the population reaches 50,000.
The initial size of a culture of bacteria is 1500. After one hour the bacteria count...
The initial size of a culture of bacteria is 1500. After one
hour the bacteria count is 6000.
A.) Find a function n(t) = n0ert
that models the population after t hours (round your r value to
five decimal places.) n(t)=
B.) Find the population after 1.5 hours. (round answer to
nearest whole number.) n(1.5)=
C.) After how many hours will the number of bacteria reach
10,000? (round your answer to one decimal place.)
The number of bacteria after ? hours in a controlled laboratory experiment is ? = ?(?)....
The number of bacteria after ? hours in a controlled laboratory
experiment is ? = ?(?).
a. Describe the meaning of ?′(4) and include right units.
b. If the supply of nutrients is limited, which value do you
think is larger ?′(4) or ?′(15)?
the number of bacteria in millions in a petri dish t seconds after an antibiotic is...
the number of bacteria in millions in a petri dish t seconds
after an antibiotic is added is given by the function b(t) Assume
b(t) is an exponential function first point (1,12) second point
(2,2) What is the 1 unit growth factor? what is the 1 unit percent
change? How many bacteria in millions are there in the petri dish
at the moment the antibiotic is added? Find the function of B(t)
How long does it take the number of...
(1 point) The count in a bacteria culture was 200 after 15 minutes and 557 after...
(1 point) The count in a bacteria culture was 200 after 15
minutes and 557 after 25 minutes. Assume the growth can be modelled
exponentially by a function of the form Q(t)=A e rt Q(t)=Aert ,
where t t is in minutes. (a) Find the relative growth rate, with at
least the first 5 digits after the decimal point entered correctly:
r= r= equation editor Equation Editor (b) What was the initial size
of the culture? Round your answer to...
(1 point) The count in a bacteria culture was 600 after 10 minutes and 11613 after...
(1 point) The count in a bacteria culture was 600 after 10
minutes and 11613 after 20 minutes. Assume the growth can be
modelled exponentially by a function of the form
Q(t)=AertQ(t)=Aert, where tt is in minutes.
(a) Find the relative growth rate, with at least the first 5 digits
after the decimal point entered correctly:
r=r=
equation editor
Equation Editor
(b) What was the initial size of the culture? Round your answer to
the closest integer.
equation editor
Equation...
point) The count in a bacteria culture was 500 after 10 minutes and 32518 after 30...
point) The count in a bacteria culture was 500 after 10 minutes
and 32518 after 30 minutes. Assume the growth can be modelled
exponentially by a function of the form Q(t)=A e rt Q(t)=Aert ,
where t t is in minutes. (a) Find the relative growth rate, with at
least the first 5 digits after the decimal point entered correctly:
r= r= equation editor Equation Editor (b) What was the initial size
of the culture? Round your answer to the...
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