AI.F-LE.A.1.a
Prove that linear functions grow by equal differences over equal intervals, and that exponential functions grow by equal factors over equal intervals.
Example Problems
A small farm has 120 hens. Each month, the farm acquires 5 additional hens.
Which kind of function (exponential, linear, or neither) best models the relationship between time and the number of hens?
Which kind of function (exponential, linear, or neither) best models the relationship between time and the number of hens?
Tanya has a valuable stamp collection worth .
Each decade the collection's value increases by .
Which kind of function (exponential, linear, or neither) best models the relationship between time and the collection's value?
Each decade the collection's value increases by .
Which kind of function (exponential, linear, or neither) best models the relationship between time and the collection's value?
A newly discovered star has an initial brightness of 500 lumens.
Each month, the star's brightness decreases by .
Which kind of function (exponential, linear, or neither) best models the relationship between time and the star's brightness?
Each month, the star's brightness decreases by .
Which kind of function (exponential, linear, or neither) best models the relationship between time and the star's brightness?
Khan Academy ResourcesRewrite exponential expressionsInterpret time in exponential modelsEquivalent forms of exponential expressionsInterpret change in exponential models: changing unitsInterpret change in exponential models: with manipulationInterpret change in exponential modelsInterpreting change in exponential modelsInterpreting change in exponential models: changing unitsInterpreting time in exponential modelsInterpreting change in exponential models: with manipulationRewriting exponential expressions as A⋅BᵗEquivalent forms of exponential expressions

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