# College Algebra Chapter 4 – Flashcards

## Unlock all answers in this set

question
exponential functions are in the form of
f(x)=a^x
question
positive and not one
question
domain of an exponential function
all real
question
a^x is unique and real
true
question
if a^b=b^c b=?
c
question
if a >1 and m<n than, a^m_a^n
<
question
if 0<a<1, and m<n, than a^m_a^n
>
question
(ab)^x =
a^xb^x
question
(a^x)^y =
a^xy
question
a^0 =
1
question
a^xa^4 =
a^x+4
question
(a^x)/(a^y) =
a^x-y
question
(9/4)^3/2 what is the numerator and denominator of the exponent mean
denominator means square root the number numerator means cube the number
question
range of an exponential function
(0, infiniti)
question
are exponential functions continuous
yes
question
horizontal asymptote of a decreasing function
x axis as x? infiniti
question
horizontal asymptote of a increasing function
x axis as x? negative infiniti
question
3 main points in which the graph of an exponential function passes through
(-1, 1/a), (0,1), (1,a)
question
increasing function means that a is
greater than 1
question
decreasing function means that a is
in between 0 and 1
question
each exponential function f is not one to one
false
question
how many x-intercepts does the graph of f(x) = a^x have?
none
question
the x axis is a horizontal asymptote for every exponential function of the form
f(x)= a^x
question
a fee charged for borrowing a lenders money
interest
question
original amount of money borrowed
principal
question
symbol for interest rate
r
question
simple interest formula
I=prt
question
symbol for principal
p
question
to get the total amount what must one do after solving the formula?
add the total interest and principal amounts
question
what is the compound interest formula
A=P[(1+(r/n)]^nt
question
(A) stands for
final amount
question
r stands for
ANNUAL rate of interest
question
n stands for
number of times interest is compounded each year
question
t stands for
time in years
question
what is the inflation formula?
P=P?(1+r)^t
question
in terms of inflation, what does p stand for?
value after inflation
question
in terms of inflation, what does p? stand for?
initial price
question
in terms of inflation, what does r stand for?
ANNUAL rate of interest
question
deflation formula
p=p?(1-r)^t
question
what is the formula for e
e=(1+1/n)^n
question
What is the continuous compound interest formula
A=Pe^rt
question
What two factors have to match in a financial word problem?
rate and time
question
What is the natural exponential function?
f(x)=e^x
question
formula for exponential growth
a(t)=a?e^kt
question
formula for exponential decay
a(t)=a?e^-kt
question
what happens if k is greater than 0?
uphill
question
what happens if k is less than 0?
downhill
question
y = log?x if and only if
x=a^y
question
log?a=
1
question
log?a^x=
x for any x>0
question
log10=
1
question
log10^x=
x
question
a^log?^x=
x for any x>0
question
ln e=
1
question
ln e^x=
x
question
e^lnx=
x
question
if anything is positive, ln e^anything =
the anything
question
if anything is positive, e^lnanything =
the anything
Get an explanation on any task
Get unstuck with the help of our AI assistant in seconds
New