[MA2015] AL1 (9-12) 45 :
45 ) Represent data on two quantitative variables on a scatter plot, and describe how the variables are related. [S-ID6]
a. Fit a function to the data; use functions fitted to data to solve problems in the context of the data. Use given functions or choose a function suggested by the context. Emphasize linear, quadratic, and exponential models. [S-ID6a]
b. Informally assess the fit of a function by plotting and analyzing residuals. [S-ID6b]
c. Fit a linear function for a scatter plot that suggests a linear association. [S-ID6c]
[MA2019] AL1-19 (9-12) 27 :
27. Interpret the parameters of functions in terms of a context. Extend from linear functions, written in the form mx + b, to exponential functions, written in the form abx.
Example: If the function V(t) = 19885(0.75)t describes the value of a car after it has been owned for t years, 1985 represents the purchase price of the car when t = 0, and 0.75 represents the annual rate at which its value decreases. [MA2019] AL1-19 (9-12) 25 :
25. Construct linear and exponential functions, including arithmetic and geometric sequences, given a graph, a description of a relationship, or two input-output pairs (include reading these from a table). [MA2019] AL1-19 (9-12) 24 :
24. Distinguish between situations that can be modeled with linear functions and those that can be modeled with exponential functions.
a. Show that linear functions grow by equal differences over equal intervals, while exponential functions grow by equal factors over equal intervals.
b. Define linear functions to represent situations in which one quantity changes at a constant rate per unit interval relative to another.
c. Define exponential functions to represent situations in which a quantity grows or decays by a constant percent rate per unit interval relative to another.