figuring the population growth during a particular year

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yanarains

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It is estimated that t years from now, the population of a certain community will be

P(t) = 32 -
9/(6t+1) thousand people.

By how much will the population actually increase during the 18th years?

By deriving 32 I get =0

So this is how I figured out this problem:

-[(0)(6t+1)] - [(9)(6)]/ (6t+1)2 = -(-54)/(6t+1)^2= 54/(6t+1)^2

Since I am figuring the population increase DURING the 18th yr. I must also find what happened during the 17th yr. then minus the two. P(18)-P(17) then multiply that answer by 1000 I should come up with the answer I am looking; however I don't

54/(6(18)+1)^2 = 54/11881
54/(6(17)+1)^2 = 54/10609
=-5 ( this is my answer rounded to the nearest whole number.)

What exactly is wrong here?


Thanks again for all your help. Hope I got the grouping right this time!
 
yanarains said:
By how much will the population actually increase during the 18th years?
Click to expand...
That's got to be a typo. Ask your instructor whether you're supposed to find the increase during "the eighteen years" (plural) or "the eighteenth year" (singular).

Thank you! :D

Eliz.
 
yanarains said:
By deriving 32 I get =0
Click to expand...
I'm sorry, but I don't know what this means...? I mean, yes, if you differentiate "32" you will get "0", but what does this mean, especially in the context of the exercise...? :oops:

You have a function, P(t), which gives you the population P after t years. To find the increase over the course of the eighteenth year, wouldn't you find P(18) - P(17)? :idea:

Eliz.
 
i mean by subtracting the time during the 17th and 18th years then this should give me what the increase was during the 18th year.
therefore
P(18)54/(6(18)+1)^2 = 54/11881
P(17)54/(6(17)+1)^2 = 54/10609
since we are talking about population by thousands I multiply both of the years by 1000
=-5 ( this is my answer rounded to the nearest whole number.)

the answer is 5.

I hope this helps. this question is really confusing to me.

thank you for helping me
 
yanarains said:
i mean by subtracting the time during the 17th and 18th years then this should give me what the increase was during the 18th year.
therefore
P(18)54/(6(18)+1)^2 = 54/11881 ..... from where are you getting 54 - what are you doing?
P(17)54/(6(17)+1)^2 = 54/10609
since we are talking about population by thousands I multiply both of the years by 1000
=-5 ( this is my answer rounded to the nearest whole number.)

the answer is 5.

I hope this helps. this question is really confusing to me.

thank you for helping me
Click to expand...
 
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