# Find the value of N

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#1
The adult population of a town is 25,000 at the end of Year 1.

A model predicts that the adult population of the town will increase by 3% each year, forming a geometric sequence.

(a) Show that the predicted adult population at the end of Year 2 is 25,750

(b) Write down the common ratio of the geometric sequence

The model predicts that Year N will be the first year in which the adult population of the town exceeds 40,000.

(c) Show that: (N-1)log1.03 > log1.6

(d) Find the value of N

Please could I have help with the method for part (d)

Thanks!
0
2 years ago
#2
(Original post by Buzzz1325)
The model predicts that Year N will be the first year in which the adult population of the town exceeds 40,000.

(c) Show that: (N-1)log1.03 > log1.6

(d) Find the value of N

Please could I have help with the method for part (d)

Thanks!
Where's the model??

Difficult to help when half the info is missing.
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#3
(Original post by RDKGames)
Where's the model??

Difficult to help when half the info is missing.
Sorry forgot that bit!

The adult population of a town is 25,000 at the end of Year 1.

A model predicts that the adult population of the town will increase by 3% each year, forming a geometric sequence.

(a) Show that the predicted adult population at the end of Year 2 is 25,750

(b) Write down the common ratio of the geometric sequence
0
2 years ago
#4
(Original post by Buzzz1325)
Sorry forgot that bit!

The adult population of a town is 25,000 at the end of Year 1.

A model predicts that the adult population of the town will increase by 3% each year, forming a geometric sequence.

(a) Show that the predicted adult population at the end of Year 2 is 25,750

(b) Write down the common ratio of the geometric sequence

Anyway, you just take the inequality from part (c) and solve it for . Part (d) just requires you to take the first integer value that satisfies that inequality.
1
#5
(Original post by RDKGames)

Anyway, you just take the inequality from part (c) and solve it for . Part (d) just requires you to take the first integer value that satisfies that inequality.
Okay so by solving the inequality I get: 16.9006.....

Therefore N = 17? as its the closest that satisfies the inequality
0
2 years ago
#6
(Original post by Buzzz1325)
Okay so by solving the inequality I get: 16.9006.....

Therefore N = 17? as its the closest that satisfies the inequality
It's not which N is closest that you need, it's the smallest integer N that satisfies the inequality. This means you are going to want to always "round up". (e.g. if solving gave you 16.3 you would *still* want to take N = 17).

If you're not sure, it's a pretty good idea to actively check what you get when N=16 and N=17. It's easy to have your answer be "one too small" or "one too big" by accident with these questions.
2
#7
(Original post by DFranklin)
It's not which N is closest that you need, it's the smallest integer N that satisfies the inequality. This means you are going to want to always "round up". (e.g. if solving gave you 16.3 you would *still* want to take N = 17).

If you're not sure, it's a pretty good idea to actively check what you get when N=16 and N=17. It's easy to have your answer be "one too small" or "one too big" by accident with these questions.
Okay, that makes perfect sense. I'll note that for future questions. Thank you so much for your help!!
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