Question

A bacterial population starts with 10,000 bacteria and grows at
a rate proportional to its size. After 2 hours there are 40,000
bacteria.

a) Find the growth rate k. Round k to 3 decimal places. b) Find the
number of bacteria after 5 hours.

c) When will the population reach 1 million?

d) What is the doubling time?

Answer #1

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 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?

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...

If a bacteria population starts with 125 bacteria and doubles in
size every half hour, then the number of bacteria after t
hours is
n = f(t) = 125 ·
4t.
(a) Find the inverse of this function.
t = log4(t125)
Explain its meaning.
a The inverse function gives the population after half an hour
has passed.
b The inverse function gives the population after 4 hours have
passed.
c The inverse function gives the number of hours that have...

A bacteria culture starts with 1000 bacteria and grows at an
exponential rate. After 3 hours there will be 3000 bacteria. Give
your answer accurate to at least 4 decimal places
(a) Express the population P after t hours as
a function of t.
(b) What will be the population after 2 hours?
(c) How long will it take for the population to reach 1310?

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.

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?

The population of a town grows at a rate proportional to the
population present at time t. The initial population of 500
increases by 20% in 10 years. What will be the population in 30
years? (Round your answer to the nearest person.)How fast is the
population growing at t = 30? (Round your answer to two decimal
places.)

a
culture starts with 9000 bacteria. after one hour the count is
10100
a.) find relative growth rate of the bacteria. round answer to
4 decimal places
b.)find the number of bacteria after 2 hours (answer must be
an integer)
c.)after how many hours will the number if bacteria
double?

The initial size of the bacteria is 1000. After 3 hours the
bacterium count is 5000.
a. Find the function to model the bacteria population after t
hours.(Round your r value to four decimal places.
b. Find the population after 6.5 hours. Round your answer to the
nearest whole number.
c.When will the population reach 14,000? Round your answer to
one decimal place.

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