# Find the value of N

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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!

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!

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#2

(Original post by

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!

**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!

Difficult to help when half the info is missing.

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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

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#4

(Original post by

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

**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.

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(Original post by

Ah cool, though I didn't read your last sentence in your original post.

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.

**RDKGames**)Ah cool, though I didn't read your last sentence in your original post.

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.

Therefore N = 17? as its the closest that satisfies the inequality

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Okay so by solving the inequality I get: 16.9006.....

Therefore N = 17? as its the closest that satisfies the inequality

**Buzzz1325**)Okay so by solving the inequality I get: 16.9006.....

Therefore N = 17? as its the closest that satisfies the inequality

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.

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(Original post by

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.

**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.

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