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Exponential and Logarithmic Functions flashcards
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- What is initial value and base?Exponential Growth and Decay
- The starting quantity and repeated growth factor.
- What is y at t=0?Exponential Growth and Decay
- A because b⁰=1.
- What is decay factor?Exponential Growth and Decay
- A multiplier below one describing exponential decay.
- Does a 20% loss subtract the same amount each period?Exponential Growth and Decay
- No, it subtracts a share of the changing amount.
- What is percent change and context?Exponential Growth and Decay
- A percent change converted to a multiplicative factor.
- Why identify the period length?Exponential Growth and Decay
- Monthly and yearly rates are not interchangeable without conversion.
- What is logarithm definition?Logarithms as Inverses
- The inverse operation of exponentiation.
- Can log_b(0) be real?Logarithms as Inverses
- No, real logarithm arguments must be positive.
- What is equivalent forms?Logarithms as Inverses
- Two notations for one base-power relationship.
- What base values are allowed?Logarithms as Inverses
- Positive bases other than one.
- What is logarithm graph?Logarithms as Inverses
- A graph obtained by reflecting an exponential across y=x.
- Why is x=0 excluded?Logarithms as Inverses
- The logarithm input must be positive.
- What is product rule?Logarithm Properties and Equations
- The logarithm identity for positive factors.
- Can log_b(M+N) split the same way?Logarithm Properties and Equations
- No, there is no general log-sum rule.
- What is quotient and power rules?Logarithm Properties and Equations
- Two logarithm transformations with domain conditions.
- Why require positive arguments?Logarithm Properties and Equations
- Real logarithms are undefined for zero or negative inputs.
- What is solving and checking?Logarithm Properties and Equations
- Domain-aware checking of a logarithmic equation.
- Can algebra produce an invalid candidate?Logarithm Properties and Equations
- Yes, manipulating logarithms can conceal a forbidden argument.
- What is compound growth?Exponential and Logarithmic Models
- An exponential model for recurring proportional change.
- What does a model base encode?Exponential and Logarithmic Models
- The factor applied during each time interval.
- What is half-life?Exponential and Logarithmic Models
- An exponential decay measure by equal half periods.
- What remains after two half-lives?Exponential and Logarithmic Models
- One quarter of the initial amount.
- What is logarithmic time?Exponential and Logarithmic Models
- Finding an exponent from a target amount.
- Why check target and initial value signs?Exponential and Logarithmic Models
- The real logarithm argument must be positive.