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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.

2 Answers

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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

Explanation:

User Beena Shetty
by
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5 votes
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.
User Deadkarma
by
7.8k points
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