8th grade math problem! Simple!?

Question

1) A radioactive substance loses 0.5% of its mass every year. Today-end 0f 2006 we have 24.5kg of this substance.
a) how much did we have at the begining of 2006?
b) how much did we have at the beginning of 2002?

Answer 1

THANX PEOPLE>>>>>>Tanya

Answer 2

0.5%=0.5/100=0.005
So if it loses 0.005, then you have 1-0.005=0.995 left.
If x is the amount you had at the beginning of the year

0.995 x = 24.5 so x=24.5/0.995=24.623

Keep dividing by 0.995 until you get all the way back to 2002. Or since you know that from the beginning of 2002 to the end of 2006 there are 5 years, you can also write it exponentially as 24.5/(0.995)^5=25.12 kg

Answer 3

There are various ways to answer this, hopefully you understand exponents!

a) For exponential decay the equation in your example is y = A(0.995)^x , where A is the initial amount and x is the number of years that have passed.

So: 24.5 = A(0.995)^1 since 1 year would have passed.
24.5/0.995 = A
24.6 = A
At the beginning of 2006 you had 24.6kg of the substance.

b) 24.5 = A(0.995)^5
24.5/(0.995)^5 = A
25.1 = A
At the beginning of 2002 there was 25.1 kg of the substance. THis is assuming exponential decay!

Answer 4

I'll answer a and get you started on b.

If you lose .5% every year, then at the end of the year, you have 100% - 0.5% = 99.5% of what you had at the beginning.

Since now you have 24.5 kg, this must be 99.5% of what you had at the beginning of the year.

(amount at beginning of 2006) x 99.5% = 24.5

So divide both sides by .995, and you find out that you had 24.62 kg at the beginning of 2006:

(amount at beginning of 2006) x 99.5% / 99.5% = 24.5 kg/99.5%
(amount at beginning of 2006) = 24.62 kg

To find out how much you had at the beginning of 2005, you do the same exact thing:

(amount at beginning of 2005) x 99.5% / 99.5% = 24.62 kg / 99.5%
(amount at beginning of 2005) = 24.85 kg

So just keep doing that over and over until you get to the beginning of 2002.