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March 18th, 2017, 06:36 PM  #1 
Member Joined: Mar 2017 From: Tasmania Posts: 36 Thanks: 2  I do not think enough info or is given or is abstract
Question 11 Within the first ten years of construction the population of rats in a sewer system can be modelled by the equation N=N_0 e^kt. 2 years after construction there are 118 rats and 4 years after construction there are 1392 rats. a) Show that k≈1.234 (4 marks) b) How many rats were there originally? (1 mark) c) When will the population of rats reach 10,000? Give your answer to the nearest month (2 marks) Edit the N is big and 0 small like a log for example 
March 18th, 2017, 06:43 PM  #2 
Math Team Joined: Jul 2011 From: Texas Posts: 2,610 Thanks: 1293 
$N = N_0 e^{kt}$ $1392 = N_0e^{4k}$ $118 = N_0e^{2k}$ divide the first equation by the second ... $\dfrac{1392}{118} = e^{2k}$ ... use logs to determine $k$, then use either of the original equations to determine $N_0$ once you have $k$ and $N_0$, determining $t$ when $N=10000$ should be no problemo. 
March 18th, 2017, 07:46 PM  #3 
Member Joined: Mar 2017 From: Tasmania Posts: 36 Thanks: 2 
Thank you Skeeter so much the N0 was rly confusing me


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