College Algebra

Question

The​ half-life of radium is 1690 years. If 30 grams are present​ now, how much will be present in 450 ​years?

Answer 1

Hello, thank you for taking the time to post your question!

The underlying half-life formula that you want to use here is

N(t) = N0 (1/2)^(1/T)

For this particular scenario the values are

N_0 = 30

t = 450 years

T = 1690 years

N(t) = N(450) = what we are solving for

Plugging that into the formula should yield

N(450) = 30(1/2)^(450/1690)

=24.94 grams

That means that after 450 years, the 30 grams will be down to 24.94 grams

I hope that helps you get moving in a better direction on this type of question! Feel free to reach out if you have any additional questions beyond that :)

Answer 2

Let A(t) = amount of radium in t years

A(t) = 30e^-kt

15 = 30e^-1690k

Solve for k.

Then, using the value of k found above, evaluate 30e^-450k.

Answer 3

We can simply use the exponential decay formula;

Amount Remaining = Initial Amount * (1/2)^(Time / Half-life)

N ( t ) = N ( 0 ) × 0. 5 ( t / T )



30 grams * (1/2)^(450 / 1690) = Amount

Amount ≈ 30 grams * (0.5)^(0.266) = 23.19 grams