Evidence of Understanding

**use rate of change to define exponential functions**(*focus on base 2, 10, and e)*- identify an asymptote and justify its existence
- explain why an exponential function does not have turning points (mins or maxs)
- distinguish exponential growth from decay from a graph, table, sequence, or situation
- identify quantities and words that indicate exponential growth or decay

- analyze situations, graphs, and tables to justify an exponential function model
*(versus other models)*- introduce
**the natural base (base e)**to model situations that continuously change

- introduce
- given 3+ data points, calculate the
**base**(growth or decay rate) of the exponential function

**create representations of exponential functions***(focus on base 2, 10, and e)*- identify the initial value and common ratio of change from a situation, sequence, table or graph
- generate an exponential graph, table, explicit function rule, or recursive function rule
- connect features of exponential functions across representations
- match an exponential function rule with a sequence, situation, table or graph
- Ex: recognize “an 8% annual increase” models exponential growth with a base of 1.08

**evaluate exponential functions***(focus on base 2, 10, and e)*- calculate
__exact__output values given an input - evaluate an expression or equation written in function notation from a graph, table, or equation
- Ex: evaluate f(3) by looking at the points on graph or in the table

- analyze a situation to consider viable and nonviable domain and range values
- compare end behavior of the exponential function with the limits of the situation
- Ex: continuous exponential functions have no limits on the domain but in a situation there may be limits to how much the outputs can grow or decay

- calculate

Develop conceptual understanding:

asymptote, exponential growth, exponential decay, natural base e, base

Supporting terms to communicate:

function, independent, dependent, input, output, domain, range, ratio, initial value, function rule, function notation, end behavior, intercept, rate of change