Question

The half-life of radium is 1690 years.If 10 grams is present now, how much will be present in 50 years?

Answer 1

Do you know the formula for half life?

Answer 2

i do not

Answer 3

thats all i really need

Answer 4

Use the given information to find the decay rate constant, then you'll have the function fully described and can calculate\[\frac{A_0}{2}=A_0e^{1690k} \implies k=\frac{-\ln2}{1690} \approx 4.1(10^{-4})\].From here, you should be able to substitute into the decay function and evaluate.

Answer 5

Do you understand all the in between steps? I had a different version of the formula but @AnimalAin has the same basic idea :)

Answer 6

i do but does the same thing apply for if you are trying to find the half life of a equation

Answer 7

Look at it this way. Suppose we start (at time zero) with Asub0 units. After the half life, we have half that amount. I put that fact into the decay function, and it left me with only one variable, k. I solved for that, and am now ready to substitute the value I got into the decay function and evaluate for t=50.

Answer 8

Oh nvm, gotcha.

Answer 9

So when we substitute into the decay function.....\[A(t)=A_0e^{-4.1(10^{-4})t} \implies A(50)=10e^{-2.05(10^{-2})} \approx 9.8 g\]