Exponential Relationships flashcards

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Compare growth typesLinear versus Exponential Change: Use the same time in both rules before comparing.
When should I use additive change?Linear versus Exponential Change: Predict a linear sequence from a constant difference.
What method supports compare growth types?Linear versus Exponential Change: difference at t = E₀b^t − (L₀+dt)
Multiplicative changeLinear versus Exponential Change: Exponential change repeatedly multiplies.
Additive changeLinear versus Exponential Change: Linear change adds the same amount each step.
What must I check in linear versus exponential change?Linear versus Exponential Change: Equal differences indicate linear change only for equal input intervals; equal ratios indicate exponential change
What method supports multiplicative change?Linear versus Exponential Change: E(t)=E₀b^t, b>0
What method supports additive change?Linear versus Exponential Change: L(t)=L₀+dt
When should I use compare growth types?Linear versus Exponential Change: Compare linear and exponential outputs at a specified time.
When should I use multiplicative change?Linear versus Exponential Change: Predict an exponential sequence from a constant ratio.
Solve for an initial amountExponential Growth and Decay Models: Undo the whole repeated multiplier.
When should I use growth factors?Exponential Growth and Decay Models: Evaluate a repeated growth model.
What method supports solve for an initial amount?Exponential Growth and Decay Models: A₀=A(t)/b^t, b>0
Decay factorsExponential Growth and Decay Models: Retain the stated fraction of the current amount each time.
Growth factorsExponential Growth and Decay Models: Each increase applies to the new amount.
What must I check in exponential growth and decay models?Exponential Growth and Decay Models: A growth factor is 1+r and a decay factor is 1−r; use a consistent time unit
What method supports decay factors?Exponential Growth and Decay Models: A(t)=A₀(1−r)^t, 0<r<1
What method supports growth factors?Exponential Growth and Decay Models: A(t)=A₀(1+r)^t
When should I use solve for an initial amount?Exponential Growth and Decay Models: Recover the start from a later exponential value.
When should I use decay factors?Exponential Growth and Decay Models: Evaluate a repeated decrease model.
Rate at a different intervalInterpreting Initial Values and Growth Factors: Read how much time makes the exponent rise by one.
When should I use initial value interpretation?Interpreting Initial Values and Growth Factors: Find the model value at time zero.
What method supports rate at a different interval?Interpreting Initial Values and Growth Factors: b^(t/k) = (b^(1/k))^t
Read the percent rateInterpreting Initial Values and Growth Factors: Subtract one from a growth factor to get the fractional increase.
Initial value interpretationInterpreting Initial Values and Growth Factors: At time zero the power equals one.
What must I check in interpreting initial values and growth factors?Interpreting Initial Values and Growth Factors: The coefficient is the output at exponent zero; the rate depends on the unit represented by one exponent step
What method supports read the percent rate?Interpreting Initial Values and Growth Factors: growth percent = 100(b−1)
What method supports initial value interpretation?Interpreting Initial Values and Growth Factors: A(0)=A₀
When should I use rate at a different interval?Interpreting Initial Values and Growth Factors: Interpret an exponent measured in several time units.
When should I use read the percent rate?Interpreting Initial Values and Growth Factors: Convert between an exponential factor and a percent change.
Compatible bases with offsetsSolving Exponential Equations with Compatible Bases: Common bases turn the equation into a linear equation in the exponent.
When should I use equal-base equations?Solving Exponential Equations with Compatible Bases: Solve by equating exponents for an injective exponential base.
What method supports compatible bases with offsets?Solving Exponential Equations with Compatible Bases: a^(px+q)=a^(rx+s) ⇒ (p−r)x=s−q
Rewrite compatible basesSolving Exponential Equations with Compatible Bases: Convert both sides to powers of the same number first.
Equal-base equationsSolving Exponential Equations with Compatible Bases: Same valid base means the exponents must match.
What must I check in solving exponential equations with compatible bases?Solving Exponential Equations with Compatible Bases: Match powers only after obtaining equal positive bases other than 1
What method supports rewrite compatible bases?Solving Exponential Equations with Compatible Bases: (a^m)^x=a^(mx)
What method supports equal-base equations?Solving Exponential Equations with Compatible Bases: b^u=b^v ⇒ u=v for b>0, b≠1
When should I use compatible bases with offsets?Solving Exponential Equations with Compatible Bases: Solve a linear exponent equation after rewriting both sides.
When should I use rewrite compatible bases?Solving Exponential Equations with Compatible Bases: Express a power equation using one common base.
Several compounding periods per yearCompound Interest and Repeated Percent Change: Divide the nominal rate across periods and count all periods.
When should I use compound interest?Compound Interest and Repeated Percent Change: Evaluate repeated interest growth without deposits.
What method supports several compounding periods per year?Compound Interest and Repeated Percent Change: A=P(1+r/m)^(mt)
Repeated percentage changesCompound Interest and Repeated Percent Change: Each new percent acts on the updated amount.
Compound interestCompound Interest and Repeated Percent Change: Interest can earn more interest in later periods.
What must I check in compound interest and repeated percent change?Compound Interest and Repeated Percent Change: Use the stated compounding frequency and distinguish nominal annual rate from the per-period rate
What method supports repeated percentage changes?Compound Interest and Repeated Percent Change: A_final=A₀(1+r)(1−s)
What method supports compound interest?Compound Interest and Repeated Percent Change: A=P(1+r)^t
When should I use several compounding periods per year?Compound Interest and Repeated Percent Change: Use the per-period interest rate and number of periods.
When should I use repeated percentage changes?Compound Interest and Repeated Percent Change: Multiply distinct percent-change factors in order.
Equivalent time-unit representationsEquivalent Exponential Forms and Different Time Intervals: Convert time inside the exponent, not just in the label.
When should I use convert to a longer interval?Equivalent Exponential Forms and Different Time Intervals: Raise a short-interval factor to the number of intervals.
What method supports equivalent time-unit representations?Equivalent Exponential Forms and Different Time Intervals: A·B^(t/k)=A·(B^(1/k))^t
Convert to a shorter intervalEquivalent Exponential Forms and Different Time Intervals: Take a root to undo repeated multiplication.
Convert to a longer intervalEquivalent Exponential Forms and Different Time Intervals: Several short periods combine by multiplying factors.
What must I check in equivalent exponential forms and different time intervals?Equivalent Exponential Forms and Different Time Intervals: Changing the time unit changes the factor and exponent together; do not divide a factor by the interval length
What method supports convert to a shorter interval?Equivalent Exponential Forms and Different Time Intervals: unit factor=B^(1/k)
What method supports convert to a longer interval?Equivalent Exponential Forms and Different Time Intervals: k-period factor=b^k
When should I use equivalent time-unit representations?Equivalent Exponential Forms and Different Time Intervals: Adjust the exponent when the input time unit changes.
When should I use convert to a shorter interval?Equivalent Exponential Forms and Different Time Intervals: Take a root of a longer-interval factor.