Chapter 4.2, Problem 8E

In each of the following problems, find an exponential function of the form $f\left(t\right)=y_0{b}^t$ to model the given data. (See Examples 3 and 4.)

Personal Consumption Expenditures Medicare expenditures were $110 billion in 1990 and $646 billion in 2015. (Data from: Centers for Medicare and Medicaid Services.)

Let $t=0$ corresponds to the year 1990, and find a model for these data.

According to the model, what were the Medicare expenditures in 2012?

If the model remains accurate, estimate Medicare expenditures for 2025.