8-34,
In previous chapters you used models to estimate actual behavior. Creating a linear model for
scattered data gave you a mathematical way to describe the data and to make predictions.
The amount of money in an investment account earning simple or compound interest, such as the
situations in problem 8-33, can be modeled with step functions. Writing equations for step functions
can be very complicated. However, we can model the step functions with continuous functions we
are already familiar with. From now on in this course, we will use continuous functions to model
situations, unless indicated otherwise.
a. Think about the growth and the starting point of the investment accounts earning simple and
compound interest in this lesson. Model each of the two graphs of step functions you created in
problem 8-33 with an equation. Let y represent the money in the account after 2 years.
b. Check that your equations produce the same values as in the tables in problem 8-32. If your
models do not match the tables, correct your equations.
c. Use your models to predict how much your original $1000 investment would be worth at the
end of 20 years.
d. Why are the equations considered a model instead of a representation of the actual behavior?
Is there an advantage to using the model to make predictions?
e. What interest rate would the bonds with simple interest need to earn so that you would earn the
same amount in both accounts after six years? After 20 years? Show how you know