Thread: doubling

please help me with this maths question

moores law states that the number of transistors on an intergrated circuit will double every 18 months can be expressed as

P = Po * 2t/18

wher Po is the number of transistors on a circuit and P is the number of transistors t months after the Po

if the number on a intergrated circuit was 4000 in 1971
calculate:

(i)the number of transitors in 1980
(ii)when did the numbers of transitors break the 1,000,000 mark?

thank you for any help

p.s i already think i know how to do this but i cant be 100% sure

Hello, red55!

Moore's law states that the number of transistors on an integrated circuit
will double every 18 months can be expressed as: .P .= .Po·2^{t/18}
where Po is the number of transistors on a circuit
and P is the number of transistors t months after the Po.

If the number on a integrated circuit was 4000 in 1971, calculate:

(a) The number of transitors in 1980
(b) When did the numbers of transitors break the 1,000,000 mark?

In 1971 (t = 0), Po = 4000
. . Hence, the function is: .P .= .4000·2^{t/18}


(a) From 1971 to 1980 is 9 years = 108 months.

Therefore: .P .= .4000·2^{108/18} .= .4000·2^6 .= .256,000


(b) When was P = 1,000,000 ?

We have: .4000·2^{t/18} .= .1,000,000

Divide by 4000: .2^{t/18} .= .250

Take logs: .ln[2^{t/18}] .= .ln(250)

Then: .(t/18)·ln(2) .= .ln(250)

Hence: . t .= .18·ln(250)/ln(2) .= .143.384117 months .≈ .12 years


Therefore, the 1,000,000 mark was reached in 1983.

thanks for the help
much appreciated