Arithmetic Growth Rate Video Lecture | Science for ACT

hello friends this video on plant growth
and development part 4 is brought to you
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okay so now the question is rate of
plant growth
so at what rate but at what speed a
plant grows how fast or how slow a plant
grows how can we measure that that
whether the plant is going slow or the
plant has go too fast or how is it so
let us discuss about the rate of plant
growth it is the increase in science per
unit time now why are we discussing this
is I told you before that growth is
something which is measurable so now we
are actually trying to see how well can
we measure growth and in order to
measure it when we need to know the
speed of growth how fast it is growing
now different plants have different rate
of growth some plants grow really fast
whereas some of the plants take a lot of
time to grow so that is why you would
have observed that if you bring
different plants to your house right
some of the plants they will grow very
fast later you plant it today then after
three days you can actually see some
growth you can actually see a noticeable
increase in size but there are some
other plants where even if you plant it
or if you put the seeds today it will
actually take a lot of time to grow so
it depends from one plant to another
what would be their rate of growth or
how fast will they grow
now growth rate can be of two categories
they are categorized into two types one
is arithmetic growth rate and the other
one is geometric growth rate so these
are the two types of growth rate
actually so some plant parts show
arithmetic growth rate whereas some of
the plant parts should show mental
growth in that your vector growth rate
is more common which you see in most of
the aspects of a plant growth so however
we will discuss about both the types of
growth arithmetic root first and then
take up geometric growth now the name is
quite interesting at least for me
ultimately growth rate now when we are
talking about the growth rate for plan
why do we have a term like this at
automatic right now with the DS two
terms arithmetic and geometric geometric
can you do I am able to recall something
which you have studied in your
mathematics in your junior classes you
would have talked about arithmetic
progression and geometric progression
right so that this is something which is
which comes under your mathematics you
remember the series some there are some
series which are in AP that is
arithmetic progression there are some
serious which isn't cheating it is
geometric progression so that is where
then these names have been taken from
now why they have been named after AP +
GP that we will be able to understand
very soon so let us see what happens in
arithmetic growth rate so in this kind
of growth rate only one daughter cell
divides others mature so the catch here
is only one daughter cell divides so let
us suppose you have a parent cell it
divides into two daughter cells
now those two daughter cells will not
divide only one of them will divide
further right so this is how it will
happen let us suppose this is where the
division starts let us take for example
okay now both of these cells are
daughter cells they are formed from some
other cell now both of them will not
divide at a time now suppose this one
this cell divided so it formed two cells
this is one daughter say this is another
daughter cell okay now please do not
consider this cell right now this is not
dividing currently so this particular
cell divided it formed two daughter
cells okay now both of them will not
divide further the one which is orange
in color will divide further while the
one which is yellow in color
we'll start to differentiate that is it
will start to become matured so right
now it isn't the meristematic feels when
a cell divides it isn't the meristematic
phase but after being divided this new
cells which are formed they need to get
matured right so that process is called
differentiation so now this cell will
get matured when this cell will divide
further so in the next step what will
happen now this cell is that as it is
this daughter cell is as it is it has
not divided so this cells
differentiating but this one will divide
further into two daughter cells so this
divided further into two daughter cells
this is one this is another again in
this case one daughter cell will divide
at the other one will keep on
differentiating so if you see here this
daughter cell is this one this one is
this one and this one will divide
further to form two daughter cells right
so you understand the process so if you
see at at one time it is only one
daughter cell which will divide not both
the daughter cells so if you look at
this process what is happening initially
to how many cells did you have initially
you had two cells correct total number
of cells is two in the next step you had
three cells in the next step you had
four cents in the next step you had five
cells so now if you allow this process
to continue further so the next step you
will have six cells so if you see there
is increase in one cell at each step so
that is how the growth is taking place
so it is increasing only one per step
right now if you remember your
mathematics what was arithmetic
raishin electronic progression was any
such series where the difference between
the consecutive numbers were equal for
example a series like this 1 2 3 4 5 6
etc so here 2 minus 1 is 1 3 minus 2 is
1 4 minus 3 is 1 so the difference is
same so this is this is an arithmetic
series similarly if you take an example
of 3 5 7 9 11 and so on so this is again
an arithmetic series because the
difference is 5 minus 3 which is 2 again
7 minus 5 which is 2 again 9 minus 7
which is 2 so this is also an arithmetic
series
so wherever any series where the growth
happens automatically that is known as
an emetic growth reading so it got its
name from these kind of series because
here also the growth happens linearly so
one cell gets added in this example at
least you can see that one cell gets
started at a time so with time now as
the steps are happening time is also
increasing so with increase in time the
number of cells of course increases
because the growth rate is increasing
but it increases linearly and that is
why it is known as an automatic growth
rate now these kind of growth rate is
seen in the elongation of route so if
you see the route again at the root tip
you have the meristematic soon after
that you will have the elongation zone
and then you have the maturation zone
right so the elongation of the zone
happens by this type of growth rates and
as alpha improves it now let us try to
look at automatic growth rate
graphically now based on whatever we
have discussed so far let us suppose
this is at initial time that is HT is
equal to 0 how many cells
you had two cents now as the time
increases now what are these like booty
I mean I'm just not taking any unit
right now I just want to show you how
the graph would look like for this kind
of a growth rate let us suppose this is
second this this is just an example that
it does not mean that in one second only
one cell will increase in a plant that
was not the case I'm just taking you an
example right so the time is increasing
here and the number of cells which have
formed is increasing here right now if
you plot a graph taking time on the
x-axis and the number of cells on the
y-axis
so this number of cells will actually
determine growth in this case right so
let us suppose this is zero one two
three four five six and in here one two
three four five and six right
so now I have become easy for us to plot
it so when time is equal to zero number
of cells is two so when time is zero
number of senses to services my first
point next my time is my number of
senses tree so in time is five number of
senses means same appointed time to
number of cells fours time to number of
sense for time three number of cells
five time for number of cells six so
these are the points which you have
brought the based on the data which you
have right so if you join all these
points together what you get you get a
linear curve right so arithmetic growth
whose always represented by a linear
Club curve so the growth happens or the
growth increases linearly so that is
known as arithmetic
great so they say that is growth per
unit time so this is how an arithmetic
growth curve looks like now let us look
at arithmetic growth rate mathematically
so if you look at it mathematically how
would with me so this is a linear curves
or a linear equation you can say so
mathematically it is denoted by n T is
equal to n 0 plus R T where T what does
LT n represents the length at time T so
at time T n 0 represent the length at
initial time that as as T is equal to 0
right so here in this graph this
represents time and this represents L so
whatever we have considered as number of
cells that number of cells was just a
parameter so that is written as L so n
represents the length so as I said
growth can be determined by a number of
parameters one of them is length one of
them is the number of cells so here L
has been taken as a standard convention
so this represents n naught this value
that is the value of length at time T is
equal to 0 so this particular value
denotes L naught plus R into T what does
I R as the growth rate which would be
nothing but the slope of this line so
our denotes the growth rate and T
denotes the time correct so this is how
we can denote it mathematically that is
L T is equal to L naught plus RT thank
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