Question

MEDAL AWARDED someone please help :'( i'm stuck
2.2. A sample of radioactive material has been decaying for 5 years. Three years ago( at 2 years), there were 6.0 grams of material left. Now (at 5 years), there are 5.2 grams of material left.

a. Write two point from this problem: _________ and _________
b. Using point-ratio form, y=y1b^x-x1, plug in the two points and solve for the ratio, b. Show all steps
c.Write an exponential equation in point-ratio form for this situation
D.Define your variables (include units)

Answer 1

e. Use your equation to determine how much material will be left after 50 years from the beginning so x=50
f. what is the half-life of this material? That means when will there be half the original amount?

Answer 2

Work that I've done
a. two points are (2, 6.0) and (5,5.2)
b.6.0=5.2^5-2
c?
D?
and from there i'm just lost on e and f

Answer 3

I figured I'd answer this because I know half life mathematics pretty well.
However, I don't know it from a point of view that can express all the terms used in calculus.
Here's a good link for half-life calculations: http://www.1728.org/halflife.htm

6 grams two years ago 5.2 grams now
half-life = elapsed time * log (2)/ log (beginning amount/ending amount)
half-life = 2 years * 0.3010299957 / log (6/5.2)
half-life = 2 years * 0.3010299957 / 0.0621479067
half-life = 9.6875345096 years

Answer 4

no haha this is just basic algebra 2 :)

Answer 5

e.
Ending Amount = Beginning Amount / 2^n
where 'n' is the elapsed time divided by half life

Let's use the 2 year amount of 6 grams as the beginning time.
Ending Amount = 6 g / 2^(50years) / 9.6875345096 years
Ending Amount = 6 g / 2 ^ 5.1612719367
Ending Amount = 6 g / 35.7847237346
Ending Amount = 0.1676693118 grams

Answer 6

f. half-life has already been calculated 9.6875345096 years

Answer 7

omgg thank you so much! From a-d i did a and b

Answer 8

okay - only trouble is I only know how to express this stuff in plain English instead of "two-point" or "point-ratio" terms.

Answer 9

oh i see.. yea it's just referring back to the equation

Answer 10

Still, wouldn't it be better if they worded these problems so you could actually understand them?

Answer 11

yea haha it's just a and b seem understandable from c and d it's just confusing

Answer 12

You already have done parts c and d?

Answer 13

I have a guess for c. i think it's 5.2=6.0b^5-2

Answer 14

I could make a guess for part 'c' but I have NO idea about expressing it in "point-ratio" form.

Answer 15

Well thank you so much you've done a whole lot already.. again thanks so much for your time :)

Answer 16

u r welcome - glad I saw your posting -I had a feeling I might be able to help.

Answer 17

:))

Answer 18

okay see you later