Question

The half-life of a substance is how long it takes for half of the substance to decay or become harmless (for certain radioactive materials). The half-life of a substance is 123 days and there is an amount equal to 150 grams now. What is the expression for the amount A(t) that remains after t days, and what is the amount of the substance remaining (rounded to the nearest tenth) after 365 days?

Answer 1

You know we are going to have an exponential equation.
\[A(t)=A_0 e^{kt}\]
where A_0 is the present amount of substance
and the is time in days

Answer 2

we are given when t=123 days we have A(t) is half the present amount of substance

Answer 3

A(t) = 150(0.5)t/123, 19.2 grams remaining
A(t) = 150(0.5)123t, 1.4 grams remaining
A(t) = 123(150)(0.5)t, 0.0 gram remaining
A(t) = 150(0.5)123/t, 118.8 grams remaining

Answer 4

\[\frac{A_0}{2}=A_0 e^{k 123}\]
solve for k

Answer 5

I'm new to this.. I don't know how

Answer 6

you should see you can divide both sides by A_0
and write
\[\frac{1}{2}=e^{ 123 k}\]
can you solve this for k?