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Exponents and Exponential Functions flashcards
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- What does product of powers mean?Integer Exponents
- Multiplying powers with a common base.
- May exponents be added for different bases?Integer Exponents
- No, not by this rule.
- How would you define quotient and zero exponents?Integer Exponents
- Rules for dividing powers of the same nonzero base.
- Why exclude x=0 from a denominator?Integer Exponents
- Division by zero is undefined.
- What is meant by negative exponents?Integer Exponents
- Reciprocal meaning of a negative exponent.
- Is 2^(−3) equal to −8?Integer Exponents
- No, it equals one eighth.
- What does coefficient and power mean?Scientific Notation
- A normalized coefficient times a power of ten.
- Can the leading coefficient be 25 in normalized form?Scientific Notation
- No, its absolute value must be below ten.
- How would you define large and small numbers?Scientific Notation
- Place-value conversion between decimal and scientific form.
- What does 10^(−3) equal?Scientific Notation
- One thousandth.
- What is meant by operations in notation?Scientific Notation
- Applying product-of-powers to scaled numbers.
- Why renormalize after multiplying?Scientific Notation
- The resulting coefficient may fall outside the required interval.
- What does constant multiplicative factor mean?Exponential Growth
- A pattern with a constant ratio above one.
- How is growth different from a linear pattern?Exponential Growth
- Linear change adds a constant amount.
- How would you define growth rule?Exponential Growth
- An initial value and repeated growth factor.
- What does a represent at t=0?Exponential Growth
- The initial output.
- What is meant by percent growth?Exponential Growth
- Converting a percentage increase into a multiplier.
- What factor corresponds to 20% growth?Exponential Growth
- 1.20.
- What does decay factor mean?Exponential Decay
- A repeated multiplicative decrease.
- Does decay subtract the same absolute amount each step?Exponential Decay
- No, the removed amount usually shrinks.
- How would you define half-life model?Exponential Decay
- A repeated halving pattern.
- What remains after two half-lives?Exponential Decay
- One quarter of the starting amount.
- What is meant by percent decrease?Exponential Decay
- Converting a percentage decrease into a multiplier.
- What factor corresponds to 25% decay?Exponential Decay
- 0.75.
- What does constant difference mean?Linear Versus Exponential Change
- The defining discrete signature of linear change.
- Does a constant difference imply a constant ratio?Linear Versus Exponential Change
- Generally no.
- How would you define constant ratio?Linear Versus Exponential Change
- The defining discrete signature of exponential change.
- Does a constant ratio mean equal differences?Linear Versus Exponential Change
- Generally no.
- What is meant by model selection?Linear Versus Exponential Change
- Choosing a reasonable rule from evidence and assumptions.
- Why be cautious outside observed data?Linear Versus Exponential Change
- The original pattern may not continue.