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

Answer:

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

Step-by-step 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%: $r= \frac{25}{100} =0.25$.
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 $A$:
$64=A(0.75)^{x}$
$A= \frac{64}{0.75 ^{x} }$
Notice that $A$ will depend on the number of ours $x$.