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VCE Stuff => VCE Mathematics => VCE Mathematics/Science/Technology => VCE Subjects + Help => VCE General & Further Mathematics => Topic started by: xD_aQt on October 17, 2010, 08:36:55 pm

Title: Q's
Post by: xD_aQt on October 17, 2010, 08:36:55 pm

Number Pattern:

Bacteria C spreads through another town infecting 25 people the first day, 40 people the next day, and after that the number of people infected each day increases by 20% of the number infected the previous day.  How many people will have been infected by bacteria C by the end of the 20th day?

Any help? :P

Title: Re: Q's
Post by: stonecold on October 17, 2010, 08:38:18 pm

They are trying to trick you.  Just let 40=t1, and find the number of people for day 19.

Title: Re: Q's
Post by: xD_aQt on October 17, 2010, 08:44:43 pm

So which formula do I put it into?

Title: Re: Q's
Post by: stonecold on October 17, 2010, 08:45:11 pm

geometric with ratio of 1.2

Title: Re: Q's
Post by: xD_aQt on October 17, 2010, 08:49:33 pm

I get 6190 but the answer says 6215 :S

Title: Re: Q's
Post by: stonecold on October 17, 2010, 08:56:58 pm

Quote from: xD_aQt on October 17, 2010, 08:49:33 pm

I get 6190 but the answer says 6215 :S

Yeah, then you've gotta add on the initial 25 people.  Not a bad question actually.  Could come up on the exam...

Title: Re: Q's
Post by: stonecold on October 17, 2010, 09:00:14 pm

Yeah, but you have to discount the first day, because it is not part of the sequence, then add it on again at the end.  As you are discounting the 1st day, you need to drop from n=20 to n=19.  If you leave n=20, then add on the 25 from the beginning, then you have really found the 21st day.

Title: Re: Q's
Post by: xD_aQt on October 17, 2010, 09:02:53 pm

Ooo nice I get it :)

Title: Re: Q's
Post by: xD_aQt on October 17, 2010, 09:16:30 pm

Another question:

In a certain city, the population increases by 0.45% each year because of births, and by a fixed number of 5000 per year due to migration.  In this city, 2400 people die each year.  If the population was 20,000 at the beginning of 2010, which one of the following is closest to the population at the beginning of 2020?

Title: Re: Q's
Post by: sam.utute on October 17, 2010, 09:42:06 pm

Correct me if I'm wrong.

P(n) = 1.0045 * P(n-1) - 2400, P(0) = 5000

Just use your calculator and sub in 5000 first, the 1.0045*Ans-2400 repeatedly, til you get to the beginning of 2020 (which is after 10 years). Sorry, I don't have a calculator on me :P, can't tell you the answer.

Title: Re: Q's
Post by: TyErd on October 18, 2010, 12:32:28 am

i get an answer of 47451.3 so 47451 people. is that right?

Title: Re: Q's
Post by: xD_aQt on October 18, 2010, 04:15:44 pm

Yeah, 47451 is right :) cheers