00:02
Hello students, let us solve this question.
00:03
So in this question hypothetical data on the bird species richness from tropical island off the coast of brazil it is given.
00:13
And on the basis of the given hypothetical data, we have to answer some of the questions.
00:18
For example, first we have to draw two graphs.
00:22
So we have to plot a graph.
00:29
So we have to graph the data on standard axis, on standard also, we can say arithmetic axis, and we have to take on the x -axis, we have to take area.
00:51
On the y -axis, you have to take number of bird species.
00:58
Sp is for species.
01:00
Then you have to re -plot this graph, re -plot the graph, but this time we have to take natural log by taking natural log.
01:29
And in this, on the x -axis we have to take the natural log of the area.
01:40
And on the y axis, we have to take the natural log of number of bird species.
01:52
Then we have to determine the value of c and z with the help of two equations.
02:08
S is equal to c, a to the power z, or natural log of s is equal to natural log of c plus z times natural log of a.
02:24
Also, we have to.
02:29
It is then given that there is another island.
02:34
There is another island whose area is given to us.
02:42
Area is given as 1 ,200 square miles.
02:52
We have to find the number of bird species in this island, number of bird species.
03:06
So now let us look at the table that has been given in the question to solve.
03:11
So what is the table given in the question? island's area is given island area in square mile and the number of breeding bird species number of breeding bird species is given so island area all of this is in square miles so 75 square mile, 2 .70 square mile, 6 .90 square mile, sorry, this is 6 .40 square miles, then 861 .00 square mile, then 0 .33 square mile.
04:06
And the number of breeding birds, here is 13, then 9, then 10, then 18, then 7, then 17, then 7.
04:16
So we have to first plot this on a graph.
04:21
So let us draw a graph.
04:22
So let us plot on this graph on the basis of the hypothetical table that is given.
04:29
So if you remember on the x -axis which is this, this is your x -axis, this is your y -axis.
04:37
On the x -axis we need to plot the area and on the y -axis we need to plot the number.
04:46
Of breeding birds or the number of birds i will write number of breeding birds so on the x -axis area let us write this 400 square mile 600 square mile 800 square mile 8000 square mile and so on on the y axis, let us write the number, we are taking multiples of 2, 24, 6, 8, 10, 12, 14, 16, 18, 20.
05:43
That much is enough because if you go back to the table given in the question, the highest number of breeding bird species is only 18.
05:53
So now we will simply plot the points and draw the line.
06:02
So as you can see, the lowest number of breeding bird species is 9.
06:12
So we'll start with that.
06:15
So 9 would be somewhere here between 10 and 8.
06:20
So it would be somewhere here.
06:25
After that, you have, if you look at the next one, next.
06:30
One is what after 9 we can take 10 after 9 we can take 10 so 10 would be somewhere here then after this we also have 7 so 7 would be very very very close to the y axis after that we have only 13 and 18 left so where would be our 13 13 is somewhere here it would be before before 200 of course somewhere slightly here and then we have 18 which which is somewhere after 800 so it is what 861 861 so it is going to be somewhere here so now we will join these so this is a rough graph so this is our first graph now let us draw the second graph in which we have to take log on the natural log both on the x and the y axis now this is our second graph so here on the x axis this time you have natural log of area and on the y axis you have natural log of number of bird species so let us number them first this is going to be my 1 2 3 4 5 6 7 minus 1 minus 2 minus 4 then this is going to be 0 .5 1 1 .5 2 and 3 and 3 .5 so now if we put 5 plot the graph...