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 1965 represent the initial time, t = 0. Round the nearest hundredth, if necessary.
a. Linear Model: Y = 6495x + 50
b. Exponential Model: Y = 50(2.048^x)
2. In 1970, about 1800 transistors could fit on the semiconductor. Given this information, which model for Moore's Law is correct? Explain.
a. Exponential model because when x = 5, y = 1800
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?
a. 50, 100, 200, 400, 800, 1600
b. Geometric because it is multiplied by 2.
4. Write a rule for the nth term of the sequence.
a. an = 50(2^n-1)
5. This sequence is known as "Moore's Law." Summarize Moore's Law in your own words.
a. Every year you can fit twice the number of transistors on a circuit.
6. In the 1970s, Moore revised his prediction to say that the number of transistors would double every two years. How does this affect the rule for your sequence?
a. This means it doubles every 2 years instead of every year.
7. Write a rule for a sequence that represents the number of transistors that could fit on a 1-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.
a. (51,200)2^n-1/2
n = 42
b. 75,925,012,500
a. Linear Model: Y = 6495x + 50
b. Exponential Model: Y = 50(2.048^x)
2. In 1970, about 1800 transistors could fit on the semiconductor. Given this information, which model for Moore's Law is correct? Explain.
a. Exponential model because when x = 5, y = 1800
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?
a. 50, 100, 200, 400, 800, 1600
b. Geometric because it is multiplied by 2.
4. Write a rule for the nth term of the sequence.
a. an = 50(2^n-1)
5. This sequence is known as "Moore's Law." Summarize Moore's Law in your own words.
a. Every year you can fit twice the number of transistors on a circuit.
6. In the 1970s, Moore revised his prediction to say that the number of transistors would double every two years. How does this affect the rule for your sequence?
a. This means it doubles every 2 years instead of every year.
7. Write a rule for a sequence that represents the number of transistors that could fit on a 1-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.
a. (51,200)2^n-1/2
n = 42
b. 75,925,012,500