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53 Cards in this Set
- Front
- Back
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has a relative rate of change (%) |
Exponential Modeling |
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What r and t need to be in exponential formula |
variables that need similar units in formula Q = Q0 (1 + r)^t |
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What is the double time formula for Q = Q0 (1 + r)^t |
Q = Q0 (2)^t/Tdouble |
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What is the double time formula for Q = Q0 (1 + r)^t
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Q = Q0 (1/2)^t/Tdouble
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rapid growth; can't go on forever |
Define Exponential Growth |
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Equation: 70/growth% |
Tdouble formula |
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initial value X 2^t/Tdouble= new value |
Formula to predict a population's growth after time |
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birth rate - death rate = |
world growth rate formula |
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the maximum population for an environment to sustain the particular species for long periods of time.
Population growth rate gradually decreases as the population approaches the carrying capacity |
Define logistic growth |
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logistic rate = exponential rate (1- (population size / carry capacity)) |
logistic growth formula |
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In a function, y= |
F(x) |
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What letter is often used to represent the independent variable |
The letter X |
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What letter is often used to represent the dependent variable |
The letter Y |
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Name three ways to model a function |
Data table, graph, and equasion |
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the possible values that make sense for the independent variable |
Define Domain |
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the possible results of the dependent variable |
Define Range |
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Step ?: Identify the independent and dependent variable |
Step 1 of creating a function |
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Step ?: Identify the domain and range and choose scale and lablees |
Step 2 of creating a function |
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Step ?: Make a graph using the data. Figure out an assumption on how to connect data points |
Step 3 of creating a function |
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Step ?: Before accepting the predictions of the model, look at the assumptions the model are based on |
Step 4 ofcreating a function |
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slope or rate of change is constant (absolute) and is a straight line |
Define Linear function |
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rate of change = |
slope |
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y=mx+b |
Linear function formula |
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Rules of Logarithms
Log 10^x = |
Rules of Logarithms Rule 1) = X |
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Rules of Logarithms log x 10 = |
Rules of Logarithms Rule 1) = X |
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Rules of Logarithms Log MN= |
Rules of Logarithms Rule 3) = Log M + Log N |
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Rules of Logarithms Log M/N= |
Rules of Logarithms Rule 4) = Log M - Log N |
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Rules of Logarithms Log M^R = |
Rules of Logarithms Rule 5) = R - Log M |
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the most basic possible results or an observation |
Define Outcomes |
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one or more outcomes that share a similar property |
Define Event |
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Deck of cards number of cards per suit |
Deck of cards 13 |
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Deck of cards number of red cards |
Deck of cards 26 |
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Deck of cards number of face cards |
Deck of cards 16 |
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Deck of cards number of cards in deck |
Deck of cards 52 |
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used to find outcomes for independent events |
Define multiplication rule |
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Expressing Probabilities how it is written |
Expressing Probabilities P(event) |
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Expressing Probabilities 0 means |
Expressing Probabilities the event never happens |
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Expressing Probabilities 1 means |
Expressing Probabilities The even always happens |
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based on a model where all events are equally likely. |
Define Theoretical Probability |
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the total events divided by the number of outcomes |
Theoretical Probability Formula |
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based on observations or experiments |
Define Relative Frequency or Empirical Method |
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%, the total events divided by the time of the measurement |
Relative Frequency or Empirical Method Formula |
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based on personal intuition or experience |
Define Subjective Probability |
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Probability of an event not happening P(not A)= |
Formula =1 - P(A) |
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Combining Probabilities Independent Event P(A and B) = |
Combining Probabilities P(A) X P(B) |
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Combining Probabilities Dependent Events P(A and B) = |
Combining Probabilities P(A) X P(B given A)
52/52 X 12/51 X 11/50 X 10/49 X 9/48 |
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Combining Probabilities Non-Overlapping P(A or B) = |
Combining Probabilities can't occur at the same time P(A) + P(B) |
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Combining Probabilities Overlapping P(A or B) = |
Combining Probabilities one or more occur at the same time P(A) + P(B) - P(A&B) |
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Combining Probabilities Independent Events P(A at least once in N trials) = |
Combining Probabilities 1 - [P(not A in one trial)]^n |
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Combining Probabilities
Formula =1 - P(A) |
Combining Probabilities Probability of an event not happening P(not A)= |
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independent process repeated through MANY trials, the proportion of trials that are event A will be close to the probability for event A, P(A). |
Define Law of Large Numbers |
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(value of event 1) X P(event 1) + (value of event 2) X P(event 2) = |
Expected Value Formula |
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5 to 1 odds meaning $5 win to every $1 loss in the Expected Value Formula: |
Odds aren't probability ($5) X P(event 1) - ($1) X X P(event 2) = |
