Group Homework 2 - Group Homework 2 1.4#46 1.6#22 Chapter...

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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). Carbon-14 has a half-life 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 half-life. 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 half-life)=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 Carbon-14. 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 331-year-old painting: P= P 0 e (-1.2097x10^-4)(331) P=.96075, or 96.075 % remaining. If the painting were authentic, the percentage of carbon-14 that should be remaining this year is 96.075% . Since the painting in question has 99.5% carbon-14 (given), it is a fake . Not enough time has elapsed for a larger percentage of carbon to decay.
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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 1.6 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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