Midcontinent Research for Education and Learning
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Common Core Mathematics 912
Cluster
Construct and compare linear, quadratic, and exponential models and solve problems
Grade 912
F.LE.1.
Distinguish between situations that can be modeled with linear functions and with exponential functions.
F.LE.1.a.
Prove that linear functions grow by equal differences over equal intervals, and that exponential functions grow by equal factors over equal intervals.
F.LE.1.b.
Recognize situations in which one quantity changes at a constant rate per unit interval relative to another.
F.LE.1.c.
Recognize situations in which a quantity grows or decays by a constant percent rate per unit interval relative to another.
F.LE.2.
Construct linear and exponential functions, including arithmetic and geometric sequences, given a graph, a description of a relationship, or two inputoutput pairs (include reading these from a table).
F.LE.3.
Observe using graphs and tables that a quantity increasing exponentially eventually exceeds a quantity increasing linearly, quadratically, or (more generally) as a polynomial function.
F.LE.4.
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.