Which one would you rather have?

Hello.

These answerers are correct. A more rigorous way to explain why you'd rather have the n^2 job is to take sums from n=1 to infinity. You'll find that the n^2 job gets to infinity dollars much faster than the 9000 dollars job (which is just a constant sum).

But, earning n^2 pennies a day, on the 30th day (one month) alone, you'll earn 1,073,741,824 pennies, which is already more than 9000 dollars.

The n^2 job for sure.

Because,

The first day you get 2^0 penny = 1

Second = 2^1 = 2

Third = 2^2 = 4

Fourth = 2^3 = 8

Fifth = 2^4 = 16

sixth = 2^5 = 32

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and so on upto the 30th day ( say) = 2^ (30 - 1)

= 2^ 29

When you take the summation you'll see that it crosses 9000$ easily.

Hope this helped

Note that 2^(n - 1) is: 1, 2, 4, 8, 16, 32 …

n^2 is a different sequence: 1, 4, 9, 16, 25, 64 …

2^(n - 1) starts "slower", but quickly overtakes n^2 once n gets above 7.

For n = 5

2^(n - 1) = 16

n^2 = 25

For n = 7

2^(n - 1) = 64

n^2 = 49

For n = 10

2^(n - 1) = 512

n^2 = 100

For n = 30 … one month, give or take

2^(n - 1) = 536,870,912

n^2 = 900

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The n^2 job (aslong as i know i wont be fired or layed off) because eventually id be getting over a billion dollars a day.