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Thread: help with an exponential function

  1. #1
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    Lightbulb help with an exponential function

    Hi , I need some help with the next problem

    In 1965, Gordon Moose observed that the amount of computing power possible to put on a chip doubles every two years. In 1990, there were 1,000,000 transistors per chip. How many transistors per chip were there in 2000? 1985?

    I have tried to solve it ; however, I don't know how to interpret its growth ( I mean when it doubles every 2 years). Can some help me to write a function that describes this problem? Thanks in advance!!
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  2. #2
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    Exponential growth

    Hello skorpiox
    Quote Originally Posted by skorpiox View Post
    Hi , I need some help with the next problem

    In 1965, Gordon Moose observed that the amount of computing power possible to put on a chip doubles every two years. In 1990, there were 1,000,000 transistors per chip. How many transistors per chip were there in 2000? 1985?

    I have tried to solve it ; however, I don't know how to interpret its growth ( I mean when it doubles every 2 years). Can some help me to write a function that describes this problem? Thanks in advance!!
    We need a function that gives $\displaystyle n$, the number of transistors after a time t years (measured from 1990), such that

    At time $\displaystyle t = 0, n = 10^6$

    And, since the number doubles every 2 years, at time $\displaystyle t = 2, n = 10^6 \times 2$

    At time $\displaystyle t = 4, n = 10^6 \times 2^2$

    ...and so on.

    Clearly, we are going to need something like:

    $\displaystyle n = 10^6 \times 2^{at + b}$ for some constants $\displaystyle a$ and $\displaystyle b$.

    Notice that at time $\displaystyle t = 0, n = 10^6 \times 1 = 10^6 \times 2^0$

    and at time $\displaystyle t = 2, n = 10^6 \times 2^1$

    So we want $\displaystyle t = 0$ to give $\displaystyle at + b = 0$

    $\displaystyle \Rightarrow b = 0$

    and $\displaystyle t = 2$ to give $\displaystyle at + b = 1$

    $\displaystyle \Rightarrow 2a + 0 = 1$

    $\displaystyle \Rightarrow a = 0.5$

    So the function we need is

    $\displaystyle n = 10^6 \times 2^{0.5t}$

    You now need to find the value of $\displaystyle n$ when $\displaystyle t = 10$, and when $\displaystyle t = -5$.

    Can you complete it now?

    Grandad
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  3. #3
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    thanks Grandad . I was measuring since 1965!
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