very simple math but I dont get it

[Teddy07]

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.

 

[bowrilla]

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.

[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 2^n/18 where n is the number of months in the interval you're crossing. What you need to do is multiply by 2^12/18.

[Teddy07]

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 2^n/18 where n is the number of months in the interval you're crossing. What you need to do is multiply by 2^12/18.

 

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