chapter 4 Flashcards
an exponential function
y=a (*) b ^x
what is y in y=a(*)b^x
the output
what is a in y=a(*)b^x
the initial value (y value)
what is b in y=a(*)b^x
growth/ decay factor
what is x in y=a(*)b^x
the # of cycles of growth/ decay
what is the exponential growth
b>1
what is the exponential decay
0<b></b>
how do you graph an exponential function
use an input output table w/ domains as -2,-1,0,1,2
does f(x)=1.5^x show growth or decay?
growth, 1.5>1
what formula do you use if an amount is increasing or decreasing by a constant percentage?
I=p(1+r)^t
what does I stand for in I=p(1+r)^t
y=a(*)b^x
what does the p stand for in I=p(1+r)^t
the initial value
what does r stand for in I=p(1+r)^t
rate of growth/ decay
what does the t stand for in I=p(1+r)^t
of cycles of growth/ decay
what is the growth factor
(b>1)
I+r(in decimal form)
what is the decay factor
(0<b></b>
define domain
x’s
define range
y’s
find the domain and range for and the inverse
X: 0-1-2-4-8
Y: 2-4-5-6-7
Domain: 0 x 8
range: 3
how do you write the inverse of a function f(x)=2x
f^-1(x)=1/2x
what is an exponential equation
b*=a
what is a logarithmic equation
log b ^a=x
how is 2^x=8 written as a log equation
log 2^8=x
what does a log ask?
what power of b is equal to a
2^4=16 in log
log2^16=4
log9^9=1 in exponential
9^1=9
log 4^64 evaluate
4^x=64
x=3
logb^b=
1
logb^1=
0
logb^ (mn)=
logb^m=logb^n
logb(m/n)
logb^m-logb^n
logb(m)^n
n Log b^m
logb^b^b^x=
x logb^b
x(*)1
x
b^logb^x=
x
how to solve an exponential equation
set it in terms of the same base or taking the log of both sides
how to solve a log equation
use log properties to write as single log then write in exponential form.
solve 3^2x=27
3^2x=3^3
2x=3
x=3/2
solve log,6(2x-1)=-1
6^-1=2x-1
1/6=2x-1
7/6-2=2x/2
x=7/12
how to solve an exponential equation
- write in terms of same base
2. take log of both sides of EQ
how to solve a log equation
- write a one log by applying log prop. if necessary
2. put into exponential form and solve
