What is a logarithmic & a exponetial graph?
an exponential graph has an ever increasing gradient (assuming its positive, really what i mean is the gradient doesn’t change from positive to negative or vice versa) at minus infinity going up, the gradient is just above zero, and going into the positive numbers, increases in gradient very quickly a logarithmic graph is the inverse of an exponential graph (reflect an exponential in the line y=x and you have the inverse graph) y = e^x is a special exponential graph as it differentiates to itself i.e dy/dx = e^x its used in science because mostly thats the properties displayed in the natural world like for example bacteria, you have 1 that splits to 2, those 2 to 4, 4 to 8 etc.
If you have two variables that are related to each-other in a (straight) linear way and plot them on a Linear graph you will get a straight line.eg if y=2x then you will see a relation ship so when y= 10 ,x 20 and when y=40 x = 80 etc However not everything is related in this linear way for example if y=x squared then when y= 10 x =100 and when y=40 x=1600 etc if this were plotted on a graph you would get a curve called an exponential curve.As it is a curve it is difficult to extrapolate ( extend the curve ) accurately and predict other values of data. However by using y=log x for this relationship we once again get a straight line relationship which can easily be extrapolated.
