more on exponential growth - 109 workshop 5
In your next 109 workshop you will be looking at the effect of temperature on biological rates...
Here is a graph showing how growth rate varies with increasing temperature. Between points a and b there is an exponential increase in growth rate - this means that the growth rate keeps increasing by the same factor for every jump up in temperature.
Remember what exponential increase is? Here is an example of a set of numbers that are increasing exponentially:
2,4,8,16,32,64,128....
For this example the factor by which these numbers increase each time is two - i.e. the numbers keep doubling which means the gap between them keeps getting bigger and bigger.
So back to the graph above, between a and b the growth rate is increasing exponentially with increasing temperature. The equation that describes this part of the graph can be written like this:
Where Rt2 is the rate of growth at temperature 2
Rt1 is the rate of growth at temperature 1
k is the factor by which the rate increases
t2 is temperature 2
t1 is temperature 1
(and remember the dot is a short hand way of writing a times sign -'x')
This may look a bit familiar to you, remember my last post on exponential growth? In that post I showed you where the equation for exponential growth comes from; we were looking at how the number of weeds increases exponentially over time... the equation we came up with to describe the exponential increase of weeds over time was:
Nt = Nt0 x kt
Where Nt is the number of weeds at a particular time
Nt0 is the number of weeds at time zero
k is the factor by which the number of weeds increases each week
t is time in weeks
Both of these equations are essentially the same - they both describe exponential growth. The only difference is that the top one is dealing with the exponential increase in a rate as a result of increasing temperature where the bottom one deals with the exponential increase in the number of weeds as a result of increasing time.
:)
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