Exponential and Logarithmic Function Review

Growth or Decay

100

in the equation y=ab^x, as the value of x increases, the values of y increases

What is exponential growth

200

In the equation y=ab^x, as x decreases (but not below zero) the y also decreases

What is Exponential Decay

300

the growth/decay factor in the equation y=12(0.95)^x

What is a decay factor of 5%

400

The growth/decay factor in the equation y=3(4)^x

What is a growth factor of 300%

500

Suppose you invest $1000 in a savings account that pays 5% annual interest, if you make no additional deposits, how many years will it take to get to  at least $1500

At least 9 years later

Properties of Exponents

100

The graph of -1/3 * 3^x is this translation from the parent graph y=3^x

What is a reflection across the x axis AND a compression of 1/3

200

How does the graph of y=2^(x-4) compare to the graph of the parent function y=2^x

What is a horizontal translation to the right by 4 units.

300

How does the graph of y=20(1/2)^x+10 move from the parent function y=20(1/2)^x?

What is a vertical translation of 10 units up.

400

How does the graph of y=5*0.75^x+5 compare to its parent function y=0.75^x ? 

What is a vertical shift up 5 units AND a horizontal stretch of 5

500

Suppose you won a contest at the start of 5th grade that gave you $500 and you put that $500 in an account with an interest rate of 4% each year. How much will you have when you graduate high school?

in 7 years you will have about $662

Inverses

100

the logarithmic form of 100=10²

What is log₁₀100=2

200

The value of log₈32

What is 5/3

300

The logarithmic form of 625=5⁴

What is log₅625=4

400

The evalutaion of log₂8

What is 2³

500

What is the value of log₆₄(1/32)

What is -5/6

Properties of Log and Ln

100

The expanded logarithm of log (4x/y)

What is log 4 + log x - log y

200

The single logarithm of ln32 - ln2

What is ln(32/2) or ln16

300

The name of this property tells us we can take log_bmn = log_bm + log_bn

What is the Product Property

400

The expanded logarithm for ln₃9x³

What is ln₃9 + 3ln₃x

500

What is 2 ln 15 - ln 75 written as a single natural logarithm

What is ln 3

Equations

100

The solution to the equation 4^3x=64

What is x=1

200

The solution of 6^2x=10 (round to the nearest ten thousandth) 

What is x=0.6426

300

The solution of log(x-3)+log x = 1

What is x=5 or x=-2

400

The solution for 4e^2x+2=16 ( to the nearest hundredth)

What is x=0.626

500

The solution of 1,200,000(0.93)^x=600,000 when using logarithms

 What is x=9.55