Relax. You have done problems like these before. Even if these problems look a bit different, just do what you can. If you’re not sure of something, please ask! You may use your calculator. Please show all of your work and write down as many steps as you can. Don’t spend too much time on any one problem. Do well. And remember, ask me if you’re not sure about something.
As you work, make a “don’t forget” list of any information you need to look up or ask about.
1.
United States ethanol production has been growing exponentially. In 1990, there were 0.9 billion gallons of ethanol produced. At that time it was estimated that production would increase 5.5% per year.
(a)
Name the variables, including units.
(b)
What is the annual growth factor?
(c)
Write an equation that describes the function.
(d)
In 2008 actual production of ethanol was 9.0 billion gallons. Is that production level higher or lower than predicted from your equation? Explain.
(e)
When does your equation predict that ethanol production was 9.0 billion gallons? Use successive approximation. Display your guesses in a table. Report the actual year.
2.
An insurance deductible is the amount you pay for any claim before the insurance company starts paying. Lee’s automobile insurance deductible started at $500, but they take off $10 for each month where he has no accidents or tickets. For example, after 1 month his deductible was $490, after 2 months it was $480, and so on.
(a)
Name the variables, including units and dependence.
(b)
Make a table showing the deductible after 6 months, 1 year, or 3 years without an accident or ticket.
(c)
When would the deductible vanish? (Meaning, when is it $0?)
(d)
Write an equation showing how the deductible decreases.
(e)
What is the slope and what does it mean in the story?
(f)
What is the intercept and what does it mean in the story?
3.
Our investment club has been tracking the performance of a biofuel company’s stock over the past year. Using an econometrics software package, we found the equation
\begin{equation*}
V =0.00004T^3 + 0.01T^2 - 0.9T + 31
\end{equation*}
which describes the value of each share of stock $\(V\) as a function of time \(T\text{,}\) measured in weeks starting exactly one year ago.
(a)
Name the variables \(V\) and \(T\text{,}\) including units and dependence.
What is the equivalent APR Cicely is paying? Use the Equivalent APR Formula. Don’t forget to report the percentage.
(c)
Cicely is working on her monthly budget. She has only $230 per month left after those car payments. If she puts that money into a bank account each month earning 2.91% interest compounded monthly, how much will she have after 5 years when the car is paid off? Use the Future Value Annuity Formula.
(d)
In 2011, Cicely was cleaning out the basement and found some savings bonds with face value $1,600 that matured in 1972 and have been earning 3% interest compounded monthly ever since. What were they worth? Use the Compound Interest Formula.
