Due: 02 December 2011
Math 1090-002
25 November 2011
Section 4.6 Homework
Instructions: Complete the following problems in the space provided. Please
show your work; write down enough so that a classmate could follow the steps
you’ve taken to arrive at the solution.
Each of the following word problems is worth 5 points, for a total of 20 points
possible on the assignment.
6. Radioactive contamination from the Chernobyl nuclear power plant accident
in 1984 was carried by winds to surrounding lands. The hay crop in neighboring
Austria was contaminated by iodine-131, a product of uranium decay with a
half-life of 8 days. It was determined that after 10 half-lives have passed, such
contamination is reduced to safe levels. What percent of an initial amount of
iodine-131 contamination is safe using this guideline? Use the radioactive decay
model
y(t) = y0 ert .
1
14. A certain insect population grows exponentially (with base e) at a rate of
2%. From an initial population of 500 insects, how long does it take for the
population to triple in size? How long does it take for an initial population of
1000 insects to triple in size?
2
18. When table salt is dissolved in water, it dissociates into sodium and chloride
ions, according to an exponential decay model. If 25 pounds of salt is placed in
a container filled with water, after 10 hours 15 pounds is still undissolved. How
long will it take to reduce the undissolved amount of salt to 2 pounds?
3
21. A relatively recent earthquake in Salt Lake City measured 5.1 in magnitude
on the Richter scale. In the distant past, Salt Lake was hit by an earthquake
of large magnitude that measured 7.5 on the Richter scale. How much greater
was the intensity of the past earthquake compared to the more recent one? Use
the formula
M = log
I
I0
,
where M is the magnitude of the earthquake, I is the intensity of the earthquake
and I0 = 10−3 is the zero-level earthquake, or the minimum intensity that can
be felt.
4