Section9.2Applications of Exponential Models Activities
Activity9.2.1.
The 1938 Fair Labor Standards Act established a federal minimum wage of $0.25 per hour in the United States. The federal minimum wage has been increased many times since it was established in 1938.
The federal minimum wage increased much more frequently between 1938 and 1981 then it has since 1981. If we use only the federal minimum wage data up to 1981, we find that it increased, on average, at about 6.14% per year during that time period. The data between 1938 and 1981 is also closer to fitting an exponential model than if we look at all of the data up to 2009.
Prices increase over time due to inflation. Inflation varies from year to year, but we can calculate average annual inflation and use it to study price increases over a time period. Inflation also varies between categories of goods and services: some types of goods and services have experienced faster inflation than others in recent years.
between 1985 and 2025 was about 2.78% per year. Use this information to find a formula to calculate the amount of money you’d have needed, \(t\) years after 1985, in order to have the same buying power as $100 in 1985.
Set up a new formula to calculate the average college tuition at a private, four-year univeristy, \(t\) years after 1985, assuming average college tuition increased at the overall average inflation rate.
The average cost of college tuition at a private, four-year university in 2024 was about $43,400 (2025 numbers weren’t yet available when this problem was written!). Was the average inflation rate for college tuition higher, lower, or about the same as for the US as a whole?
Set up a new formula to calculate the price of a dozen eggs, \(t\) years after 1985, assuming this price increased at the overall average inflation rate.
, the price of a dozen eggs in September 2025 was about $2.00. Was the average inflation rate for a dozen eggs higher, lower, or about the same as for the US as a whole?
Inflation measures price increases over time. The impact that price increases due to inflation have on people’s lives depends not only on inflation itself, but also on whether or not their wages are increasing by a corresponding amount. According to the US Census Bureau 7
Use the average annual inflation rate of 2.78% per year to build a formula for the median household income \(t\) years after 1985, assuming the median household income increased at the same rate as overall inflation.
, the median US household income in 2024 was $83,730. Has the median household income increased at a faster, slower, or about the same rate as overall inflation? What does this tell you about the overall affordability of life for the median US household? Does your answer match with your intuition?
The overall average annual inflation rate in the US between 1985 and 2024 may have only been 2.78%, but the average inflation rate for private, four-year university tuition specifically was 5.15%.
Use the inflation rate for private, four-year university tuition to build a formula for the median household income \(t\) years after 1985, then use your formula to estimate the median household income in 2024.
in 1985 was $82,800. The median sales price of a US house in 2025 is about $416,900. This means that average annual inflation in house sales prices during this period was about 4.12%.
Use the inflation rate for house sales to build a formula for the median household income \(t\) years after 1985, then use your formula to estimate the median household income in 2024.
