Question

Dr. Steve is working with a new radioactive substance in his lab. He currently has 64 grams of the substance and knows that it decays at a rate of 25% every hour.

Identify whether this situation represents exponential growth or decay. Then determine the rate of growth or decay, r, and identify the initial amount, A.

Answer 1

This situation models exponential decay because the substance decays with time.

The radioactive substance decays at the rate of : 25%

r=25/100 =0.25

The initial amount of substance is 64 grams. So, . A=64

Explanation:

Answer 2

Remember that the general decay equation is:

`y=A(1-r)^(x)`
where

`y` is the amount after a time
`x`

`A` is the initial amount

`r` is the the decay percent in decimal form

The first ting we are going to do is find
`r` by dividing our decay rate of 25% by 100%:
`r= (25)/(100) =0.25`.
We also know from our problem that
`y=64`. Lets replace
`y` and
`r` in our formula:

`64=A(1-0.25)^(x)`

`64=A(0.75)^(x)`
We know now that our decay rate is 0.75, and since 0.75<1, we can conclude that this situation represents exponential decay.

Now, to find the initial amount, we are going to solve our equation for
`A`:

`64=A(0.75)^(x)`

`A= (64)/(0.75 ^(x) )`
Notice that
`A` will depend on the number of ours
`x`.