like if a computer double in speed every 1 1/2 year. then in how many years from now will computer be approximately 1000 times faster than they are now?
2006-09-11 08:57:48 · 7 answers · asked by ic2011 5 in Science & Mathematics ➔ Mathematics
about 15 years
2006-09-11 09:04:06 · answer #1 · answered by ghostbeta34 2 · 1⤊ 0⤋
You must solve
1000*x=x*(1+r/n)^(n*t),
for t
x=computer's speed
r=computer's acceleration. (the rate at which the computer's speed changes)
n=number of times the speed changes in a year (because u asked in how many years)
Solve for t by cancelling the x on both sides. And substituting n=1/(1.5) or n= 2/3 and r=4/3 (because u must convert from 1.5 years to 1 year).
1000=(1+2)^(t/1.5)
=3^(t/1.5)
=3^(t*2/3)
Take log both sides and divide both sides by log(3).
Then multiply both sides by 3/2 and you have your t.
I got t=9.43156... years or 9 years, 5 months, 5 days etc. The exact answer is impossible to measure but after 9 years, 5 months and 6 days, you can be sure that ur computer is 1000 times faster.
2006-09-11 16:37:03 · answer #2 · answered by thierryinho 2 · 0⤊ 0⤋
It take 10 'doublings' to get to x1024, so 15 years.
2006-09-11 16:06:15 · answer #3 · answered by Wundt 7 · 0⤊ 0⤋
11 years
1, 2, 4, 8, 16, 32,64, 128, 256 512 1028
2006-09-11 16:04:25 · answer #4 · answered by bkbarile 5 · 0⤊ 0⤋
A less "brute force" solution:
3/2 * log(1000) / log(2) = 14.95 years
2006-09-11 16:43:27 · answer #5 · answered by Anonymous · 0⤊ 0⤋
13 and a half years minus a few days to reach 1000 times
D.
2006-09-11 16:06:00 · answer #6 · answered by Dan S 6 · 0⤊ 0⤋
ln(1000) / ln(1.5)= (plug into a calculator or computer with appropriate software)
2006-09-11 20:01:50 · answer #7 · answered by rhino9joe 5 · 0⤊ 0⤋