Exponential Growth and Decay Functions & The Natural Base e
Logarithms and Logarithmic Functions
Transformations & Modeling of Expo. and Log Functions
Properties of Logarithms
Solving Expo. and log Equations
100
y=5^x represents exponential growth or decay
What is exponential growth? 5>1
100
Rewrite 8^(2/3)=4 in logarithmic form
What is log(base 8) 4 = 2/3
100
Describe the transformation of f represented by g
f(x) = e^-x
g(x) = e^(-5x) -8
What is a horizontal shrink by a factor of 1/5,
and a translation of 8 units down?
100
Expand log(base 8) 3xy
What is log(base 8) 3 + log(base 8)x +log(base 8)y
100
log (base 3) (2x-5) = 2
What is x=7
200
Simplify (20e^3)/(10e^6)
What is (2/e^3)
200
Find the inverse of the function:
f(x) = 8^x
What is g(x) = log (base 8) x
200
Write an exponential function whose graph passes through points (1,3) & (2,12)
What is y=.75(4)^x
200
Expand
ln (3y)/(x^5)
What is ln 3 + ln y - 5 ln x
200
Solve for x
6^x = 12
What is x = 1.387
300
1/3 e^x represents exponential growth or decay
What is exponential growth? a>0, r>0
300
Rewrite the equation in exponential form and find x.
log(base x) 36 = 2
What is x^2 = 36
x = 6
300
Write an exponential function whose graph passes through points (1,2) & (3,50)
What is y=(2/5)(5)^x
or y=.2(5)^x
300
Condense
log(base 2) 12 - log(base 2) x
What is log(base 2) 12/(x^2)
300
Solve
e^(4X-2) =16
What is X = 1.193
400
y= 3e^(-.75x) represent exponential growth or decay
What is exponential decay? a>0, r<0
400
Find the inverse of y=log(x+9)
What is y=10^x - 9
400
Write an exponential model for the pairs x, and y
x: 1, 2, 3, 4
y: 1.64, 2, 2.36, 2.72
What is y=3.60(1.43)^x
400
Use change of base to evaluate the logarithm
log (base 2) 10
What is 3.322
400
Solve
2lnx-1 = 4
What is x = 12.182
500
You deposit $1500 in an account with 7% annual interest compounded daily. What is the balance after two years?
What is $1735.39?
500
Find the inverse of y=ln2x
What is y= 1/2 e^x
500
Write a rule for g.
Let the graph be a vertical stretch by a factor of 3, followed by a translation of 6 units left and 3 units up of the graph f(x) = e^x
What is g(x) = 3e^(x+6) +3
500
Use change of base to evaluate the log
log (base 23) 42