microchip declines

every 6 mnths the price becomes 37/100 of the previous price.
37/100~ 36/100 ~ 9/25 ~1/3

after 1 year price: 81*(1/3)^2=9
after 2 years price: 9*(1/3)^2=1

hence, B

I feel scoobydooby wanted to write 33/100 in place of 37/100, but cool approximation in the end.

sanju09 wrote:The price of a microchip declines by 67 percent every six months. At this rate, approximately how many years will it take for the price of an $81 microchip to reach $1?
A. 1.5
B. 2
C. 3
D. 13
E. 13.5

Given that our number is divisible by 3, no need to approximate - quickest way will be brute force, multiplying by 1/3 each time (2/3 decrease = 1/3 of).

Start: 81
6 months: 27
1 year: 9
18 months: 3
2 years: 1

If we want to do it algebraically, the question is really asking:

If 81*(1/3)^x = 1, what's the value of x?

So, (1/3)^x = 1/81

1/(3^x) = 1/81
3^x = 81
x = 4

4*(6 months) = 2 years

Pick (b).