Math

Suppose a quantity is halvd every 18 years. use the approximate half-life formula to estimate its decay rate.

is the half life equation
y= 1/2^t1/2

2^1/2t= 1/y

t 1/2= log2 (1/y)

Where do I put 18 at?

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  1. quantity=originalamount*2-t/18
    or as you prefer
    quantity=originalamount*(1/2)t/18

  2. Where do you get the original amount and the quantity from? I am confused since the problem doesnt have anymore numbers than 18

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  3. I really don't know what the question is asking, unless it wants the "decay rate"

    quantity=oritinal amount(2t/18
    take the ln of each side
    ln(quantity)=ln(original)+t/18 * ln 2

    now take the deravative...
    1/q dq/dt=0+1/18 *ln2

    so the decay rate is
    dq/dt=q*ln2 / 18

  4. What does dq stand for and dt? sorry for all the questions

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  5. dq/dt is rate of q changing with respect to time. It is a calulus term. dx/dt is rate of change of x, and so on. That is what surprised me about the question, rate is a calculus term.

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