Expontential Growth Word Problem

M

math-a-phobic

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Feb 10, 2006
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Please help, I need to know if $1,024,000 is the solution to this word problem. :?:

Problem: You broke the king's bank!!! Your offer of accepting only pennies on the 64th square is more than the king can pay. He counter-offers this proposal. On square one he will put $500. On each successive square he will double the amount of the previous square. But for just 12 squares. How much is he offering?


I am pretty sure that the king is offering $1,024,000 but I did this by making a chart, I do not know how to derive the equation for this problem. :? Can you please help me derive the formula for this word problem? Thank you! :)
 
Here's one way of looking at it: The answer is a little more than what you

have. It appears you used something like \(\displaystyle (2000)2^{9}\).

This is just the last term. You have to add all the others before it too.

This is a geometric series with common ratio 2 and first term 500.

\(\displaystyle S_{12}=(500)\frac{1-2^{12}}{1-2}\)
 
Thank you for your speedy reply Galactus, after using the equation for S subscript 12, I received the amount of $20, 475. Is this correct? :? Thank you for your feedback, I really appreciate the help! :)
 
No, that's not quite correct. Tack 3 zeros to the end of that.
 
Thanks again for the help, but why would it be 20,475,000 instead of 204,750,000? The decimals are confusing me. :cry:
 
I'm so sorry, I should've said 2 zeros to the end of that.

What do you get when you add 2 zeros to the end of 20,475?.

I'm getting calculia. :oops:
 
I'm sorry for any trouble this may have caused you. :( I got 2,047,500 after adding two zeros to 20,475. Is this answer correct now? This problem was so....... confusing. :? Thanks again for all your help, :)
 
That is correct. :D

For that matter, let's brute force it and check.

1000(.5+1+2+4+8+16+32+64+128+256+512+1024)=2047500.

Looks like the formula works.
 
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