Flashcards in PreCalc Chapter 3 Test Deck (48)
what is the equation for exponential growth?
what does each variable stand for
A=Ie^kt and A=le^-kt
A is what you have (dependent)
I is your initial amount
e is 2.71828 (constant/base/multiplier)
k is constant of exponentialism (constant coefficient/growth rate)
and t is time (independent)
what are the logarithmic models?
An exponential growth model has the form ______, and an exponential decay model has the form_________.
y=ae^bx or A=Ie^kt
y=ae^-bx or A=Ie^-kt
in probability and statistics, Gaussian models commonly represent populations that are ___________ _____________.
a logistic growth model has the form
a logarithm is an _____
logarithmic and exponential equations are _______
the parent log has an assumed base of ____
the natural log has an assumed base of __
10 (common log)
what does e=
logarithmic graphs have a ____ asymptote (__=#) while exponential graphs of a ____ asymptote (__=#)
is e a variable?
no, it is a constant
what is true of all logarithmic graphs?
how do you restrict the domain?
how do they look?
they all pass vertical line test, always have x-intercept and asymptote
you cannot take the log of 0 or a negative number
how you know if an equation is exponential
it has a variable as an exponent
what would you do with
take the square of the number first then multiply by the implied negative one
how would you simplify 3^x-2
like terms have the same ____ and same _________
polynomial functions are examples of ___ functions
exponential and logarithmic functions are examples of nonalgebraic functions, also called _____ functions
you can use the _______ Property to solve simple exponential equations
the exponential function f(x)=e^x is called the ______ _____ function, and the base e is called the ______ base
natural exponential, natural
to find the amount A in an account after t years with principal P and an annual interest rate r compounded n times per year, you can use the formula______________.
to find the amount A in an account after t years with principal P and an annual interest rate r compounded continuously, you can use the formula _____________.
the inverse function of the exponential function f(x)=a^x is called the ______ function with base a
the common logarithmic function has base
the logarithmic function f(x)+lnx is called the ______ logarithmic function and has base _________
the inverse properties of logarithms state that logaA^x=x and
to one-to-one property of natural logarithms states that if Inx=Iny, then_______________
the domain of the natural logarithmic function is the set of __________ ________ __________.
positive real numbers
all real numbers such that x is greater than 0
to evaluate a logarithm to any base, use the ______ formula