IF.4.AIII.4
Analyze and interpret exponential functions numerically, graphically, and algebraically, identifying key characteristics such as asymptotes, end behavior, intercepts, and domain and range
Example Problems
The relationship between the elapsed time t, in years, since a sample of carbon-14 began decaying, and the remaining mass M(t) in grams is modeled by the following function:
Complete the following sentence about the half-life of carbon-14:
The sample's mass is halved every ___ years.
Complete the following sentence about the half-life of carbon-14:
The sample's mass is halved every ___ years.
The relationship between the elapsed time t, in hours, since a bacterial culture was left at room temperature, and the number of bacteria N(t) is modeled by the following function:
Complete the following sentence about the doubling of the bacteria:
The number of bacteria doubles every ___ hours.
Complete the following sentence about the doubling of the bacteria:
The number of bacteria doubles every ___ hours.
The relationship between the elapsed time t, in years, since a new car was purchased, and its resale value V(t) in dollars is modeled by the following function:
Complete the following sentence about the depreciation of the car:
The car loses 20% of its value every ___ years.
Complete the following sentence about the depreciation of the car:
The car loses 20% of its value every ___ years.
Khan Academy ResourcesRewrite exponential expressionsGraphing exponential growth & decayInterpret quadratic modelsComparing linear functions word problemsGraphs of exponential growthLinear models word problemsInterpret time in exponential modelsEquivalent forms of exponential expressionsInterpret change in exponential models: changing unitsInterpret change in exponential models: with manipulationExponential vs. linear growth over timeInterpret change in exponential modelsInterpret exponential expressions word problemsIntro to exponential functionsExponential function graphGraphing exponential growth & decayInterpret quadratic models: Factored formInterpreting change in exponential modelsInterpreting change in exponential models: changing unitsGraphs of exponential growthComparing linear functions word problem: climbInterpreting time in exponential modelsInterpreting change in exponential models: with manipulationComparing maximum points of quadratic functionsWorked examples: Forms & features of quadratic functionsComparing features of quadratic functionsWorked example: domain & range of piecewise linear functionsInterpret quadratic models: Vertex formRewriting exponential expressions as A⋅BᵗEquivalent forms of exponential expressions
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