Question

moores law predicts that the number of transistors that can be fit on a microchip will increase by 40% every year. if microchips from a given year could hold about 922,200 transistors, how many transistors could fit on a microchip 19 years later? if necessary, round your answer to the nearest whole number. transistors

Explanation:

Step1: Identify the formula for exponential growth

The formula for exponential growth is $A = P(1 + r)^t$, where $A$ is the final amount, $P$ is the initial principal amount, $r$ is the annual growth rate (in decimal), and $t$ is the time in years.
Here, $P = 922200$, $r = 0.40$ (since 40% = 0.40), and $t = 19$.

Step2: Substitute the values into the formula

Substitute $P = 922200$, $r = 0.40$, and $t = 19$ into the formula $A = P(1 + r)^t$.
So we have $A = 922200\times(1 + 0.40)^{19}$.

Step3: Calculate the value of $(1 + 0.40)^{19}$

First, calculate $1+0.40 = 1.4$. Then calculate $1.4^{19}$. Using a calculator, $1.4^{19}\approx102.4508$.

Step4: Calculate the final amount $A$

Multiply $922200$ by $102.4508$: $A = 922200\times102.4508\approx922200\times102.4508 = 94473127.76$.

Answer:

94473128