Linear, Quadratic, and Exponential Models

Distinguish between situations that can be modeled with linear functions and with exponential functions

Observe using graphs and tables that a quantity increasing exponentially eventually exceeds a quantity increasing linearly, quadratically, or (more generally) as a polynomial function.

Show that linear functions grow by equal differences over equal intervals and that exponential functions grow by equal factors over equal intervals(This can be shown by algebraic proof, with a table showing differences, or by calculating average rates of change over equal intervals).

Recognize situations in which one quantity changes at a constant rate per unit interval relative to another.

Recognize situations in which a quantity grows or decays by a constant percent rate per unit interval relative to another.

For exponential models, express as a logarithm the solution to ab(ct) = d where a, c, and d are numbers and the base b is 2, 10, or e; evaluate the logarithm using technology

Interpret the parameters in a linear (f(x) = mx + b) and exponential (f(x) = a ? dx ) function in terms of a context(In the functions above, m and b are the parameters of the linear function, and a and d are the parameters of the exponential function.) In context, students should describe what these parameters mean in terms of change and starting value.