The number of Australians who are registered organ donors when they die (A) is increasing exponentially according to the formula A=A0(0 in subscript)e^kt, where t is the number of year since 2006.
In the 12 months before the beginning of 2006, 202 registered organ donors died, and in the 12 months prior to the beginning of 2008 the number was 259.
i) In the formula A=A0ekt , show that A0(0 in subscript)=202 and k=0.124, correct to three decimal places.
ii) Using the formula, predict how many Australians who die during 2009 will be registered organ donors, that is when t=4
iii) At present there are 1388 Australian people waiting for kidney transplants. If the number of registered donor deaths continues to follow the exponential formula, when will there be no one on the waiting list? (Assume no additional people join the waiting list, and that each donor provides kidneys for exactly one person.)