Question

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?

Answer 1

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

Answer 2

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

Answer 3

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

quantity=oritinal amount(2^t/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

Answer 4

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

Answer 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.