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Showing posts from March, 2019

converting an exponential to a straight line, why and how

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Sometimes when you are dealing with an exponential graph it is just a whole lot easier to convert the exponential graph to a straight line graph (you have done this a couple of times already in 107). For example, remember this graph - it shows how growth rate increases with increasing temperature, and the part of the graph between points a and b represents exponential increase in growth rate with increasing temperature. Now remember this equation: Where  Rt2  is the  rate of growth at temperature 2 Rt1  is the  rate at growth at temperature 1 Q10  is the  factor by which the rate increases for every 10 degrees increase in temperature t2  is  temperature 2 t1  is  temperature 1 (and remember the dot is a short hand way of writing a times sign -'x') If you want to calculate Q10, how are you going to do it? You could read a couple of points off the exponential graph and enter them into the equa...

the laws of logs

In your next 109 workshop (workshop 5) you will see that an exponential equation  (that describes an exponential graph)  has been converted to a straight line equation by using logarithms.  It is going to be useful for you to be able to do this conversion yourselves - and I will go through this in my next post - but before I do that I want to make sure you are ok with how to manipulate logarithms... Here are some of the laws of logarithms: 1.  Log 10  (m x n)    =     Log 10 m +  Log 10 n proof: Log 10  (100 x 100)  =   Log 10  (10000) =   4 which is the same as: Log 10  (100 x 100)  =   Log 10 100  +   Log 10 100   =   2 + 2  =   4 2.  Log 10  (m / n)    =     Log 10 m -  Log 10 n proof: Log 10  (1000 / 100)    =     Log 10 10  =  1 ...