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Midterm 1

Math 120, Winter 2005&= nbsp; &nbs= p; &= nbsp; &nbs= p; NAME_______= ________________

SHOW YOUR WORK

1. Ex= ponential Decay. Uranium 238 has a = half life of 4.5 billion years. If= a rock sample has 72% of its initial U-238 remaining, how old is the sample?<= /p>

2. Carbo= n 14 has a half life of 5730 years. If= an initial sample has 5kg of C-14, how much will be left after 3500 years?

3. The a= mount of a light from a glowing watch decays exponentially. If the light intensity has dropped= by 50% in 2.5 hours, what is the half-life of the light?

4. From = problem 3, if it had dropped by 30% in 2.5 hours, what would be the half-life?

5. If yo= u start with a full pie and it is eaten at an exponential rate, with a doubling con= sumption time of 1 minute, how long until only 1/16 of the pie is left?

6. Expon= ential Growth. Certain bacteria double their popul= ation in 22 hours. If you start wit= h 36 bacteria, how many do you have in 45.8 hours?

7. It ta= kes the earth and sun 250 million years to orbit the center of the Milky Way galaxy= . If the distance to the center of the Milky Way from the earth is 25,000 light years what is our linear speed about the center of the galaxy in miles per hour? (note: 1 light year =3D5.879x10¹² miles) What do you think about this number?

8. Given= the following triangle, find all of the trig functions:

Hyp=3D6

Opp=3D3

9. Simpl= ify the following using trigonometric identities; show your work for full credit:

a) ₌

b) ₌

c)

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