Exponent Rules/Exponential Functions
Exponential Functions- Growth/Decay
Exponential Form/Logarithmic Form
Evaluate the expression
Solve the equation
100
In the general form of an exponential function (shown below), what does the "b" stand for?
acceptable answers:
growth/decay factor
factor
multiplier
100
In the general form of an exponential function (shown below), what does the "a" stand for?
Initial value or y-intercept
100
Write the equation in exponential form.
logab=c
ac=b
100
Write the equation in exponential form, then solve for x.
log12144=x
12x=144, x=2
100
Solve the equation.
log33x=log336
x=12
200
True or False:
If the "b" is between 0 and 1 the exponential function grows.
False
200
Describe the transformation from f(x) to g(x)
f(x)=2x
g(x)=2x-4+3
Vertical shift 3 units up
Horizontal shift 4 units to the right
200
Write the equation in logarithmic form.
ab=c
logac=b
200
Evaluate the expression.
log996
6
200
Solve the equation.
log6216=x
x=3
300
Simplify. Express your answer as a fraction.
(3x3)-2
1/(9x^6)
300
What is the decay factor of the situation below?
A phone is bought for $799.99 and loses 15% of its value each year.
0.85
300
Write the equation in exponential form.
log432=5/2
45/2=32
300
Evaluate the expression.
log8(1/4096)
x=-4
300
DAILY DOUBLE!!
Solve the equation.
log12x=(1/2)log129+(1/3)log1227
9
400
Simplify. Express your answer as a fraction.
6x^4y^-7*x^5y^8z^-3
(6x^9y)/z^3
400
The population of a booming city is growing at an exponential rate of 4.3% annually. If the population started at 265,553, what would be population be after 1 decade?
approximately 404,571
400
Write the equation in exponential form.
loge65.98=x
ex=65.98
400
Convert the logarithm to a natural logarithm and evaluate.
log61296
4
400
Solve the equation.
logroot(3)10=x
x=1/3
500
Simplify. Express your answer as a fraction.
((2x^4y)/(3x^3y^2))^-2
(9y^2)/(4x^2)
500
The spread of a virus is decreasing exponentially by 1.75% each day. If a current number of cases is 22,900, about how many cases will there be in 2 weeks?
Approximately 17885 cases
500
Write the equation in logarithmic form.
6-2=1/36
log6(1/36)=-2
500
Given that log8=0.9031, evaluate the logarithm below.
log0.00008
-4.0969
500
Solve the equation.
log5(x+4)+log58=log564
4