Question

A cell of some bacteria divides into two cells every 40 minutes.The initial population is 4 bacteria.

a: Find the size of the population after t hours. y(t)=

b: Find the size of the population after 5 hours. y(5)=

c: When will the population reach 20? T=

Answer #1

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...

Under ideal conditions a certain bacteria population is known to
double every five hours. Suppose that there are initially 200
bacteria. (a) What is the size of the population after 20 hours?
bacteria (b) What is the size of the population after t hours? P =
(c) Estimate the size of the population after 34 hours. (Round your
answer to the nearest integer.) bacteria (d) Graph the population
function. (e)Estimate the time for the population to reach 60,000.
(Round your...

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 is halving every 20 hours.
a) How long does it take the population to reduce to 10% of the
initial number?
b) Find the approximating and exact decay rate.
c) Suppose the initial population is 1,500. Find the population
of this bacteria after 2 days.

Under ideal conditions, a bacteria population (denoted
P) is known to double every 8 hours. Suppose there are initially 3
bacteria.
What is the size of the population after 40
hours?
What is the size of the population after t
hours?
Estimate the size of the population after 45 hours.
Round up to the nearest integer.

A given bacteria culture initially contains 1500 bacteria and
doubles every half hour. The number of bacteria p at a given time t
(in minutes) is given by the formula p(t)=1500e^(kt) for some
constant k. (You will need to find k to answer the following.)
a) Find the size of the bacterial population after 110
minutes.
b) Find the size of the bacterial population after 8 hours.

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.

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?

(2 pts) A population of bacteria doubles every 8 hours.
We start with 250 cells. How many will we have after 5 days. Use
the simple formula, y = ab^x where b = 2 for doubling
increment.
(2 pts) Now use the general formula. y(t) = a × e^kt. At
0 days, we have 250 cells. At 15 days with have 8,192,000 cells.
What is the rate constant in units of days^-1.
(2 pts) A scientist will recognize that 0.693...

A bacteria is found which population grows 15% every 6 hours.
Establish and solve an Initial Value Problem to express the
population of bacteria as a function of time and graph this
function. By how much does the bacteria population multiply every 4
days?
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