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# very simple math but I dont get it

Go to solution Solved by Dash Lambda,

If I understand you correctly, you're doubling it each 18-month period until you're left with 12 remaining months, then you use the ratio 12/18 directly for the last figure. The error is in that last part -You aren't multiplying by the amount of time, you're multiplying by 2n/18 where n is the number of months in the interval you're crossing. What you need to do is multiply by 212/18.

Ok, guys!

I have checked both my numbers 10 times.

CPU transistors now: 2.5 billion circuits

I shall assume that it doubles every 18 to 24 month.

How many transistors will have CPU have in 10 years?

ok pretty easy:

bottom range: 2.5*2^(10*12/24) = 80 billion

upper range: 2.5*2^(10*12/18) = 253 billion

I made a short spreadsheet to check the numbers. Bottom range is true as my table shows. However, the upper range is that I end up in year 6 with 160 billion + parts of year 7 160*12/18 as there are 12 months left. My table shows 266.66 billion. How the hell is this possible?

I don't get it why there is a difference. I spend an hour thinking of the reasons. I feel embarrassed to even ask this simple question.

I really want to understand it.

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I'd say … check your table. If it is correct I just guess there might be a rounding issue. Check steps in between as well.

Your calculation seems right to me.

Edit: You could make it easier by going for 12 years since it's divisble by 1.5 and 2 years. That gives you an integer as exponent in both cases. You range would be between 2.5*2^6 and 2.5*2^8. Your equation for your exponent is correct since it gives you those values as well. The issue has to be your spreadsheet.

Use the quote function when answering! Mark people directly if you want an answer from them!

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If I understand you correctly, you're doubling it each 18-month period until you're left with 12 remaining months, then you use the ratio 12/18 directly for the last figure. The error is in that last part -You aren't multiplying by the amount of time, you're multiplying by 2n/18 where n is the number of months in the interval you're crossing. What you need to do is multiply by 212/18.

"Do as I say, not as I do."

-Because you actually care if it makes sense.

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1 hour ago, Dash Lambda said:

If I understand you correctly, you're doubling it each 18-month period until you're left with 12 remaining months, then you use the ratio 12/18 directly for the last figure.

Yes

1 hour ago, Dash Lambda said:

The error is in that last part -You aren't multiplying by the amount of time, you're multiplying by 2n/18 where n is the number of months in the interval you're crossing. What you need to do is multiply by 212/18.

Yes, you are right. So I forgot to take into account the exponential expansion. Damn! It never crossed my mind. It makes sense but it feels counter-intuitive