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