Chapter 8 Performance Task:
Integrated Circuits and Moore's Law
In April of 1965, an engineer named Gordon Moore noticed how quickly the size of electronics was shrinking. He predicted how the number of transistors that could fit on a 1-inch diameter circuit would increase over time. In 1965, 50 transistors could fit on the circuit. A decade later about 65,000 transistors could fit on the circuit. Moore's prediction was accurate and is now known as Moore's Law. What was his prediction? How many transistors will be able to fit on a one-inch circuit when you graduate from high school?
1. Using the given information and the regression feature on your graphing calculator, create a linear and an exponential model for Moore's Law. Let 1995 represent the initial time, t=0. Round to the nearest hundredth, if necessary.
A. Linear model: y=mx+b y=6945x+50
B. Exponential model: y=ab^x y=50(2.05)^x
2. In 1970, about 1800 transistors could fit on the semiconductor. Given this information, which model for Moore's Law is correct? Explain.
Linear model: 6945(5)+50=34,775
Exponential model: 50(2.05)^5=1,810
3. Write a sequence of terms representing the number of transistors that could fit on a one-inch diameter circuit from 1965 to 1975. Is the sequence arithmetic or geometric? Why?
The sequence is geometric because the equation is being multiplied rather than added.
1965(year 1)=50
1966(year 2)=102.5
1967(year 3)=210.13
1968(year 4)=430.76
1969(year 5)=883.05
1970(year 6)=1,810.25
1971(year 7)=3711.03
1972(year 8)=7607.58
1973(year 9)=15,595.56
1974(year 10)=31,970.89
1975(year 11)=65,540.33
4. Write a rule for the nth term of the sequence.
an=50(2.05)^(n-1)
5. This sequence is known as "Moore's Law." Summarize Moore's Law in your own words.
"Moore's Law" states that approximately the number of transistors in a circuit doubles every 2 years.
6. In the 1970s, Moore revised his predictions to say that number of transistors would double every two years. How does this affect the rule for your sequence?
Our sequence shows that the number of transistors doubles every year.
7. Write a rule for a sequence that represents the number of transistors that could fit on a one-inch diameter circuit from 1975 on using Moore's revised prediction. Using that rule, predict how many transistors will be able to fit on a circuit in the year that you graduate.
y=50(2.05)^(x/2)
Since we graduate in 2017 (42 years from 1975) the number of transistors that could fit on a one-inch diameter circuit is 1761116921.9 circuits.
In April of 1965, an engineer named Gordon Moore noticed how quickly the size of electronics was shrinking. He predicted how the number of transistors that could fit on a 1-inch diameter circuit would increase over time. In 1965, 50 transistors could fit on the circuit. A decade later about 65,000 transistors could fit on the circuit. Moore's prediction was accurate and is now known as Moore's Law. What was his prediction? How many transistors will be able to fit on a one-inch circuit when you graduate from high school?
1. Using the given information and the regression feature on your graphing calculator, create a linear and an exponential model for Moore's Law. Let 1995 represent the initial time, t=0. Round to the nearest hundredth, if necessary.
A. Linear model: y=mx+b y=6945x+50
B. Exponential model: y=ab^x y=50(2.05)^x
2. In 1970, about 1800 transistors could fit on the semiconductor. Given this information, which model for Moore's Law is correct? Explain.
Linear model: 6945(5)+50=34,775
Exponential model: 50(2.05)^5=1,810
3. Write a sequence of terms representing the number of transistors that could fit on a one-inch diameter circuit from 1965 to 1975. Is the sequence arithmetic or geometric? Why?
The sequence is geometric because the equation is being multiplied rather than added.
1965(year 1)=50
1966(year 2)=102.5
1967(year 3)=210.13
1968(year 4)=430.76
1969(year 5)=883.05
1970(year 6)=1,810.25
1971(year 7)=3711.03
1972(year 8)=7607.58
1973(year 9)=15,595.56
1974(year 10)=31,970.89
1975(year 11)=65,540.33
4. Write a rule for the nth term of the sequence.
an=50(2.05)^(n-1)
5. This sequence is known as "Moore's Law." Summarize Moore's Law in your own words.
"Moore's Law" states that approximately the number of transistors in a circuit doubles every 2 years.
6. In the 1970s, Moore revised his predictions to say that number of transistors would double every two years. How does this affect the rule for your sequence?
Our sequence shows that the number of transistors doubles every year.
7. Write a rule for a sequence that represents the number of transistors that could fit on a one-inch diameter circuit from 1975 on using Moore's revised prediction. Using that rule, predict how many transistors will be able to fit on a circuit in the year that you graduate.
y=50(2.05)^(x/2)
Since we graduate in 2017 (42 years from 1975) the number of transistors that could fit on a one-inch diameter circuit is 1761116921.9 circuits.