The line graph shows the cost of inflation. What cost $10,000 in 1967 would cost the amoun...

The line graph shows the cost of inflation. What cost $10,000 in 1967 would cost the amount shown by the graph in subsequent years. (The symbol  on the horizontal axis shows that there is a break in values between 0 and 80. Thus, the first tick mark on the horizontal axis represents 1980.)

Source: U.S. Bureau of Labor Statistics

Here are two mathematical models for the data shown by the graph. In each formula, C represents the cost x years after 1980 of what cost $10,000 in 1967.

Use these models to solve Exercises.

Use model 1 to determine in which year the cost will be $80,483 for what cost $10,000 in 1967.

Formulas with rational expressions are often used to model learning. Many of these formulas model the proportion of correct responses in terms of the number of trials of a particular task. One such model, called a learning curve, is

where P is the proportion of correct responses after x trials. If P = 0, there are no correct responses. If P = 1, all responses are correct. The graph of the rational formula is shown. Use the formula to solve Exercise.