Geometric Growth Rate Video Lecture - NEET

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now let us see what is geometric growth
rate so here both the daughter cells
will continue to divide so in this case
the growth would be faster because there
only one daughter cell was dividing to
form new cells but here both will divide
to form new cells so the number of cells
formed will be more and that is why the
growth rate will also be more so it
would be something like this if you
start with two cells each of them would
divide so this divided so if you see
here this n divided to form these two
and this then divided to form these two
now again each of these poor daughter
cells when divided so this will form
these two and in this will form these
two this valve on thing is two and this
will form these two right and now you
see there are n cells which are formed
in each of them will divide further
before who cells so maybe this with one
- this one - this one - this one - so
how many cells will be formed sixteen
cells to be more in each of them will
divide further to form two two cents
each so just see how many number of
cells are being produced in this case so
as they clear the number of cells
produced here is huge in a very short
period of time huge number of cells will
produce therefore the growth rate in
these of geometric growth rate is very
very fast however when you actually look
at the growth curve with lot of
geometric growth also you will see that
the initial growth is slow when compared
to the later growth and which is
followed by a rapid growth so rapid
growth is very evident here so why is
the initial growth slow because
initially you just have less number of
cells right so that is why the growth is
comparatively lesser
as number of cells increases the growth
also increases batteries right so
initial growth will be so much later
there will be rapid growth however again
after quite some time due to limited
nutrient supply the growth rate will
slow down and the fruit will become
almost stagnant with time so initially
it will just start the process so the
initial growth will be slowed later it
will become very very fast it will
remain very fast for some time and then
again it will reach a stage where there
is not much of nutrient because see for
each of the cell to divide they all need
energy now if they are like getting
divided in this fashion just see how his
cells have been formed just in two three
steps so now when so many cells have
been formed all of them need that much
of energy as well correct
so sometimes energy is not sufficient
it's the amount of energy which is
available is not sufficient so when that
condition comes into picture the growth
rate will become stagnant so it will not
grow any further so where do we see this
type of growth rate geometric growth
rate is shown by most of the cells
tissues and organs
most of them divided by geometric growth
rate so now we will try to plot the
graph of geometric growth rate now if
you plot the graph of a geometric growth
rate this is how it looks like so this
is how the graph would look like if you
take time along the x axis and the
growth along Y axis so whichever
parameter you take on the y axis say let
us suppose the size growth in terms of
science so what happens as time
increases initially the growth is like
less so this P is the first phase
as the NAG feels so this is they'll act
it's where the group is like it is
increasing but it is quite slow the
growth rate is very slow so this lag
feels then term lag means something
which is lagging behind so this
represents the slow initial growth so
this lag phase is followed by the
exponential fields and this is that
exponential fields so if you see in this
phase the growth increases very fast
with time right so this is potential
fields with actually see rapid growth
this field is also known as lower fees
now why is it one exponential because
the growth happens its own and sheer so
it happens very very fast and this in
turn is followed by at a stationary
phase time this is the stationary phase
so this is that phase when I said no you
know cell actually end up having lack of
new lack of nutrients and you too
limited nutrient supply the growth rate
will become stagnant it will not
increase any further so these are the
three prominent phases of the geometric
growth rate curve and this curve is
known as the state boiled curve sigmoid
curve or often it is known as the S
curve like how in ease of added medical
team you have three here dub similarly
here you have the sigmoid curve or the S
curve so this is how we can represent
the geometric growth rate graphically
now this curve is often known as the
growth curve it was also part growth
curve the sigmoid curve is the most
common growth curve
because most of the cells tissues and
organs they divide by geometric rotate
so geometric growth growth rate is more
common than arithmetic growth rate in
plants so let us see geometric growth
rate mathematically as I said here the
growth happens exponentially so
therefore it is represented as W 1 is
equal to W naught e to the power RT
where W 1 W represents the size so this
is how it looked like right so this
represents size at time T is equal to T
so this would be WT is equal to W naught
so this is the initial size or you can
say size at time T is equal to 0 e to
the power RT so I this again the rate of
growth or the growth rate so this is
growth rate and T is the time right and
what does this e e is nothing but the
base of the natural logarithm that is
why we say exponent shiney so that is
how reading press it so here you can see
how fast this will increase
now as the value of the tiny changes so
it was that we actually the WT will
actually mainly he to the power
something so which is going to be a very
big fan that multiplied by the initial
size so the growth is very fast in case
of geometric growth rate now this is
known as geometric growth rate because
it is it is like the chewing to progress
in geometric progression the series used
to be something like this you have three
then you have six then you have nine so
geometric progression would be something
like this three six and twelve and half
24 and half what you need then you have
96 so this is an example of geometric
progression why because this divided by
is to again this divided by this is true
so every time whatever responding is
double here so 3 into 2 is 6 6 V 2 is 12
12 to 2 is 24 by 4 into 2 is 48 so here
this by this so everything in at each
step it gets multiplied so that is why
the volume increases very fast in a
geometric progression and that this
value is known as geometric growth rate
then so now that we have discussed about
both the types of growth rate animatic
and geometric we have come across a term
growth rate this R right so I was
defined as a growth rate now let us
discuss some very important points about
this growth rate thank you please visit
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