ALGEBRA II EXPO STORY PROBLEMS
Due Cinco de Mayo.
1. The amount of fuel used annually by each car in the US has decreased by about 2% each year
since 1980, when it was about 591 gallons.
a) Write an exponential function to model this situation.
b) Estimate the average number of gallons of gasoline used by a car in 1987.
2. The population in Wisconsin was about 4.7 million in 1980 and about 4.9 million in 1990.
a) Write an exponential function to model the population of Wisconsin over time.
When you find the growth rate, just let it be PER EVERY 10 YEARS!
b) Use the model you wrote to estimate the population in 1970.
And since you found the growth rate for every 10 years, you just need to plug in -1 year as you are going back one decade.
3. Peter Griffin puts aside $350 a month for Stewie’s college fund. After a year and a half, he
moves the money to Quahog National. They offer him two options:
1) 4.32% interest compounded continuously
2) 5.12% compounded semi annually. After 16 years, which option leaves him with more money?
4) According to the US Census Bureau, the population of Colorado in the year 1990 was
3,294,394. The population of Colorado in the year 2000 was 4,301,261. Write an exponential
equation in the form y  ab x to model the population of Colorado since 1990.
Again use 10 year periods for the x.
5) Use your equation from question 4) to predict the population of Colorado in the year:
a. 2050 (x will not be 60!)
b. 1950 (x will not be -40!)
6) Dasher is looking towards retirement. Santa gave him his bonus of $2,500. The North Pole
Bank will give him an interest rate of 3.5% compounded monthly. The South Pole Credit Union
will give him 3.12% compounded continuously. Where should Dasher put his money if he can
retire is 5 years?
7) I-123 is used in thyroid scans. It has a half life of 13 hours. Write the exponential decay
function for a 45mg sample. Find the amount remaining after 5 hours.
8) How long would it take to double an investment of $100 if given a rate of 7% and
compounded continuously? (what is double 100? Use your calc to find answer!)