Interpreting exponential functions
• Solve problems involving exponential functions in many different contexts. • Write exponential expressions in different forms. • Explain what the parameters of an exponential function mean in different contexts. • Use the properties of exponents to write expressions in equivalent forms.
In Unit A2, students worked with exponential functions in the form $f(t)=ab^t$ or $f(t)=a(1+r)^t$ and interpreted the parameters $a$, $b$, and $r$ in terms of a context. In this unit they see more complicated forms. In the previous section, students developed an understanding of different compounding intervals and continuous compounding using base $e$. The purpose of this section is to examine some of these different forms and learn to interpret the parameters in terms of a context. Students learn the concept of doubling time and see functions expressed in a form that shows the doubling time; they work algebraically with functions expressed in a form like $f(x) = A(1 + r/n)^{nt}$ that shows the compounding period; and they work with functions written with the base e, $g(x) = Ae^{rt}$ , in many continuous growth contexts. In this section they do not build functions in any of these forms.