Posted by admin | Posted in trees,shrubs | Posted on 25-04-2010
Tags: australian trees identify, identifying australian gum trees
Will reward points…….exponential and equations?
1) For each of the following circumstances, identify whether there is linear or exponential growth/decay involved. Answer the associated question, giving a formula in each case.
a) The Grass-tree (Xanthorrhoea australis) is a very slow growing native Australian plant. Its trunk has an average growth rate of 1cm per year, and it takes 10 years before a trunk starts to form. What is the age of a Grass-tree with a 1 metre high trunk?
b) The populations of Cook Islands and Niue in the South Pacific has been decreasing at an average rate of 2½% per year over the last 5 years. If the combined population was 23400 in 2007, what will be the population now, two (2) years later?
a) This is linear because it follows the form y = ax + b. In this case, x is your rate of change (1cm per year), a is the number of years passed and b is the initial number years it takes to grow. In this case, b is actually negative because it is time needed before growth. so height = years*growth-initial years needed to grow. 100 = 1*x – 10. Solve for x and you get 110 years.
b) This is exponential decay because the rate change is a function of the current population. 2.5% of 1000000 is more than 2.5% of 100, 25000 and 2.5 respectfully. This follows the form y =Ae^(-rt). Plugging in the values from the problem, y = current population*e^(-percent change*time) or y = 23400*e^-(.025*2). Remember that e is not a variable but represents the exponential function. You should get a final population of roughly 22244.
An Australian Kookaburra Bird Sitting on the Grass, With Its Wings Spread and Sunning Itself
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