Evidence of Understanding

**create exponential models and use them to solve problems (focus on base 2, 10, and e)**- create a function rule from a situation, graph, or a table of values
- recognize when to convert between exponential and logarithmic form and justify reasoning
*Example: some problems should be converted, like 3*^{x}*- 10 =19 or log*_{4}*(3x) = 3, but other problems do not require conversion to be solved, like 9*^{2x - 1}*= 81 or log*_{9}*27= x*

- convert an exponential model to a logarithm to solve for an unknown
- evaluate the logarithm using technology

- analyze a situation to consider viable and nonviable domain and range values
- interpret inputs or outputs of a function in terms of the situation it models
- compare end behavior of the exponential function with the limits of the situation
*Example: 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*

**generate an explicit or recursive rule for a sequence and use it to solve problems**- create a situation that could be represented by a given sequence
- recognize when the domain or range of a function relationship is discrete and generate a sequence that best represents corresponding outputs for a situation
*Example: Billy measures the height of a ball, dropped from 3 meters, that rebounds to 75% of its original height after each bounce.*

- determine the sum of a finite set of terms in a situation
- write arithmetic and geometric sequences using
**summation notation**and use summation notation to solve problems - expand a series written with summation notation and use the expanded form to solve for specific inputs or outputs in a situation
- create a situation that best models a given series written in summation notation

- write arithmetic and geometric sequences using

Develop conceptual understanding:

summation notation, sigma notation

Supporting terms to communicate:

function, input, output, domain, range, discrete, end behavior, asymptote, intercept, initial value, rate of change, growth, decay, logarithm, exponential, base, e, natural base, natural log, arithmetic, geometric