MII.A-SSE.B.3.c
Use the properties of exponents to transform expressions for exponential functions. For example, the expression 1.15^t can be rewritten as (1.15^(1/12))^12t ≈ 1.012^12t to reveal the approximate equivalent monthly interest rate if the annual rate is 15%.
Example Problems
The brightness of a distant supernova decreases with time t (in hours) according to
By what factor is the brightness multiplied each hour?
By what factor is the brightness multiplied each hour?
The price of a cryptocurrency follows
where t is the time in hours since tracking began. What percent is added to the price each hour?
where t is the time in hours since tracking began. What percent is added to the price each hour?
An insect population declines with time t (in years) according to
By what factor is the population multiplied each year?
By what factor is the population multiplied each year?
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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