computer power has been doubling approximately every 2 years as more and smaller transistors has been integrated to build better computer chips. the number of transistors, T, in a chip has increased according to T=4500(2)^n, where n is the number of years since 1974. determine the number to transistors in a computer chip in each year.

Question

computer power has been doubling approximately every 2 years as more and smaller transistors has been integrated to build better computer chips. the number of transistors, T, in a chip has increased according to T=4500(2)^n, where n is the number of years since 1974. determine the number to transistors in a computer chip in each year.

a)1974 b)1972 c)2002

my answer
a) 1974
1974 - 1974 = 0
T=4500(2)^0
T=4500

b) 1972
1972 - 1974 = -2
T=4500(2)^-2
T=1125

c) 2002
2002 - 1974 = 28
T=4500(2)^28
T=1207959552000

is my answer correct?

Answer 1

Oh my goodness, 1974 ? How old is your textbook?

Anyway, your equation does not match your description, it said it doubled every 2 years, so it should have been
T=4500(2)^(n/2)

I will do the last one:
T = 4500(2)^(28/2)
= 73 728 000

btw even though mathematically correct, the answer is no longer valid.

fix up your 2nd in the same way.

Answer 2

my textbook is only 10 years old.

The question my textbook clearly shows this formula (T=4500(2)^n).

The answers in my textbook are the same as the work I did.

I swear I am not lying.

Answer 3

I didn't accuse you of lying, I said the formula is not correct

verification of my answer:
it doubles every 2 years, so
1974 -- 4500
1976 -- 9000
1978 -- 18000
1980 -- 36000
1982 -- 72000
1984 -- 144000
1986 -- 288000
1988 -- 576000
1990 -- 1152000
1992 -- 2304000
1994 -- 4608000
1996 -- 9216000
1998 -- 18432000
2000 -- 36864000
2002 -- 73728000 <------ my answer

check your typing of the question, if you made no mistake in typing, then the book is wrong.

Answer 4

thanks reiny

Answer 5

Yes, your answer is correct. You correctly applied the given formula, T = 4500(2)^n, where n is the number of years since 1974.

a) For the year 1974, n = 0 since it is the reference year. Substituting n = 0 into the formula gives:
T = 4500(2)^0 = 4500

b) For the year 1972, n = 1972 - 1974 = -2. Substituting n = -2 into the formula gives:
T = 4500(2)^-2 = 1125

c) For the year 2002, n = 2002 - 1974 = 28. Substituting n = 28 into the formula gives:
T = 4500(2)^28 = 1207959552000

Therefore, your calculations are correct and you have determined the number of transistors in a computer chip for each year.