Alg1.5 Introduction to Exponential Functions
- I can compare growth patterns using calculations and graphs.
- I can use words and expressions to describe patterns in tables of values.
- When I have descriptions of linear and exponential relationships, I can write expressions and create tables of values to represent them.
- I can explain the connections between an equation and a graph that represents exponential growth.
- I can write and interpret an equation that represents exponential growth.
- I can use only multiplication to represent "decreasing a quantity by a fraction of itself."
- I can write an expression or equation to represent a quantity that decays exponentially.
- I know the meanings of “exponential growth” and “exponential decay.”
- I can explain the meanings of $a$ and $b$ in an equation that represents exponential decay and is written as $y=a \boldcdot b^x$.
- I can find a growth factor from a graph and write an equation to represent exponential decay.
- I can graph equations that represent quantities that change by a growth factor between 0 and 1.
- I can use graphs to compare and contrast situations that involve exponential decay.
- I can use information from a graph to write an equation that represents exponential decay.
- I can describe the meaning of a negative exponent in equations that represent exponential decay.
- I can write and graph an equation that represents exponential decay to solve problems.
- I can use function notation to write equations that represent exponential relationships.
- When I see relationships in descriptions, tables, equations, or graphs, I can determine whether the relationships are functions.
- I can analyze a situation and determine whether it makes sense to connect the points on the graph that represents the situation.
- When I see a graph of an exponential function, I can make sense of and describe the relationship using function notation.
- I can calculate the average rate of change of a function over a specified period of time.
- I know how the average rate of change of an exponential function differs from that of a linear function.
- I can use exponential functions to model situations that involve exponential growth or decay.
- When given data, I can determine an appropriate model for the situation described by the data.
- I can describe the effect of changing $a$ and $b$ on a graph that represents $f(x)=a \boldcdot b^x$.
- I can use equations and graphs to compare exponential functions.
- I can explain the meaning of the intersection of the graphs of two functions in terms of the situations they represent.
- When I know two points on a graph of an exponential function, I can write an equation for the function.
- I can find the result of applying a percent increase or decrease on a quantity.
- I can write different expressions to represent a starting amount and a percent increase or decrease.
- I can use graphs to illustrate and compare different percent increases.
- I can write a numerical expression or an algebraic expression to represent the result of applying a percent increase repeatedly.
- I can explain why applying a percent increase, $p$, $n$ times is like or unlike applying the percent increase $np$.
- I can calculate interest when I know the starting balance, interest rate, and compounding intervals.
- When given interest rates and compounding intervals, I can choose the better investment option.
- I can solve problems using exponential expressions written in different ways.
- I can write equivalent expressions to represent situations that involve repeated percent increase or decrease.
- I can use tables, calculations, and graphs to compare growth rates of linear and exponential functions and predict how the quantities change eventually.
- I can calculate rates of change of functions given graphs, equations, or tables.
- I can use rates of change to describe how a linear function and an exponential function change over equal intervals.
- I can determine how well a chosen model fits the given information.
- I can determine whether to use a linear function or an exponential function to model real-world data.