Math 131
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1. A baby weighed 8 pounds at birth. He gained 8 pounds in the first 5 months of life and 8.4 pounds in the next 7 months. Describe his weight in pounds as a function of his age in months, using a piecewise linear model. Give the domain and range of the function.
2. Sketch the basic function which has been transformed and the transformation on the same graph. Plot the 5 points with x - values -1, 0, 1, 2, and 3 in each.
3. (Courtesy of Dr. Lacey) At the end of World War I in the fall of 1918 an influenza epidemic hit the United States Navy. It spread to the Army, American civilians and ultimately, the world. It is estimated that by 1920, tywenty million people had died from the epidemic. The table shows the total number of civilian deaths in 45 major cities up to the end of the week ending at the date shown.
Week1 Week 3 Week 5 Week 7 Week 9 Week 11
Sept 14 Sept 28 Oct 12 Oct 26 Nov 9 Nov 23
68 1970 17914 58659 81919 90449
Use cubic regression to create a cubic model for this data. Use the week number as the x-value. Look at the graph of the model. What does this model predict for week 15?
Use logistic regression to create another model. Looking at the graphs of each model, which model would you use for extrapolation and why? Logistic is in STAT>CALC B or scroll down to the word Logistic.
What does the logistic model predict for week 15? Compare to week 11 and comment.
4. Write the formula
for each composition given 
.
5. The pH of a
substance is given by 
where 
is the hydrogen
ion concentration.
Fill in the missing information in the table.
pH 1.5 3.5 9
0.001258
6. An investment of $1500 grows at interest rate 6% compounded continuously for t years.
In how many years will the amount be a) $3000? b) $4000?
7. a) Graph 
and 
. What is the tendency (the limit) of the ratio
as x approaches
positive infinity? You can look at the
graph or at values for large x.
b) Graph 
and 
. What is the tendency of 
as x approaches
infinity?
8. Find A, B and C for the given
information: 
, The limit as
x approaches minus infinity is 3, f(0)=5,
and f(ln2)=35.
9. Find the
difference quotient 
for 
and simplify
it.