# Thread: exponential growth and decay

1. ## exponential growth and decay

1. the half life of radium is 1600a. what fraction of the radium in a sample remains after 400 a?

2. one dollar invested at 3.5% interest compounded anually doubles in 20 a. find the amount of $100 in 70 a if money earns 3.5% interest compounded annually. thank youu. 2. Originally Posted by checkmarks please help? 1. the half life of radium is 1600a. what fraction of the radium in a sample remains after 400 a? 2. one dollar invested at 3.5% interest compounded anually doubles in 20 a. find the amount of$100 in 70 a if money earns 3.5% interest compounded annually.

thank youu.
what do the a's mean?

For the first:

Use the formula $\displaystyle A(t) = A_0 e^{-rt}$
where $\displaystyle A(t)$ is the amount remaining after time $\displaystyle t$, $\displaystyle A_0$ is the intial amount, $\displaystyle r$ is the rate of decay, and $\displaystyle t$ is the elapsed time.

Also use the fact that $\displaystyle t_h r = \ln(2) \Rightarrow r = \frac { \ln(2)}{t_h}$, where $\displaystyle t_h$ is the half-life

your second question is oddly worded

3. Originally Posted by checkmarks
2. one dollar invested at 3.5% interest compounded anually doubles in 20 a. find the amount of \$100 in 70 a if money earns 3.5% interest compounded annually.
By the way, are you sure this shouldn't be "continuous" compounding? because that would fit right into the theme we have going here

4. sorry, i should've been more clear...
a represents years (it means annum)

and for the 2nd question, i thought the same. i dont know if the 1st part of the question is irrelevant or not.