Archangel
Straight line exponential graphs ...
Right
here we go...
Normally the question will give you a table of values containing two variables from which a scientists carried a certain experiment. When they plotted their values they don't get a straight line.
You will either be told two things:
1) a formula by which the variables are supposed to be connected by
2) to plot something against something
So first, they will give you the table of values:
x: 2 3 4 5 6
y: 9.2 8.8 9.4 10.4 11.6
If they tell you to plot something against something, it is much easier. For the above table of value
draw the graph of xy against x2 From the above information you know you need to find the values of x
2 and the values of xy.
Ok,
so lets find the values of x
2 first:
well simple
4, 9 , 16, 25, and 36
The values of xy
18.4, 26.4, 37.6, 52 and 69.6
Thus giving us the follow coordinates to plot:
(4,18.4) , ( 9,26.4), (16, 37.6), (25, 52) and (36, 69.6)All you have to now do is plot those points do convert your exponential graph into a straight line graph...
Then you can easily find the gradient of the graph by using
y2-y1x
2-x
1basically the gradient will be:
26.4 - 18.4 = > 8/5 or 1.6
9 - 4
To find the c - value just read off your graph
In this case, your c value should approximately be 12.2
However let me show you the algebric way of solving to find c...
Use any co ordinate, with your y - iontercept co ordinate
Which means ( 25, 52 ) and ( 0 , c )
Find the gradient of those two points
you will end up with
c - 520-25
But that equals to 1.6 (beecause we have already found the value for m)
therefore, c - 52 = - 40
c = 12
Now you can simply replace your Y = mX + C formula
which is
xy = 1.6x
2+12
just rearrange to get y in terms of x
(question taken from may/june 2003 paper 1 cambridge )