Group Homework 2
Thursday, September 21, 2006
Jessica Carlson
1.4 #46
1.6 #22
Emily Orban
Chapter Review #48
Sarah Raubinger
Page 64, Project 2
Christie Donahue
1.4
46)
We know:
•
A given picture was supposedly painted by Vermeer during his lifetime (1632
1675).
•
Carbon14 has a halflife of 5730 years.
•
The paint on the canvas contains 99.5% carbon 14.
We want to know: if the painting is an original.
We begin by using the formula for halflife. We can make P equal to one half of P
0
because we are looking for half of the initial amount.
½ P
0
= P
0
e
kt
We can insert the variables that we know and solve for k.
t (the length of the halflife)=5730
½ P
0
= P
0
e
5730k
Both P
0
’s are eliminated by dividing both sides by P
0.
½ =
e
5730k
Using the properties of logarithms, ln
e
x
=x:
ln(½)=5730k
k= 1.2097x10
–4
Now we have a formula for Carbon14.
P= P
0
e
(1.2097x10^4)t
We will use the last year that Vermeer could have possibly painted which is the year
he died: t=1675.
The time between 2006 and 1675 is 331 years.
To figure out how
much carbon would remain in a 331yearold painting:
P= P
0
e
(1.2097x10^4)(331)
P=.96075, or 96.075 % remaining.
If the painting were authentic, the percentage of carbon14 that should be remaining
this year is
96.075%
.
Since the painting in question has 99.5% carbon14 (given),
it
is a fake
.
Not enough time has elapsed for a larger percentage of carbon to decay.
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View Full DocumentGroup Homework 2
Thursday, September 21, 2006
Jessica Carlson
1.4 #46
1.6 #22
Emily Orban
Chapter Review #48
Sarah Raubinger
Page 64, Project 2
Christie Donahue
1.6
22)
a)If f(x)=ax
2
+bx+c, what can you say about the values of a, b, and c if:
(i) (1,1) is on the graph of f(x)?
If we plug in the point (1,1) to f(x)…
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 Fall '08
 BLAKELOCK
 Calculus, Sine wave, Jessica Carlson Emily Orban Sarah Raubinger Christie Donahue, Emily Orban Sarah, Orban Sarah Raubinger, Raubinger Christie Donahue

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