Exponential and Logarithmic Functions

Growth & Decay

100

An exponential function is a function with the variable as the __________________

exponent 

200

What is the exponential growth formula?

y = a(1+r)^t

300

Tom buys car for $40,300. It depreciates in value at a rate of 17% each year. What is the value of the car after 5 years. 

$15,874.33

400

Joe deposited $11,600 in an account that pays 1.75% interest. Find the balance after 3 years if the interest is compounded quarterly.

$12,223.87

500

Olivia has inherited land from her grandma. She decided the sell the land for $130,000 then place the money in a new account that earns 1.8% interest compounded monthly. How much interest will she have earned after 10 years?

$25,617.27

Converting & Evaluating

100

Convert the following to LOG form

3^x = 8

log₃ 8 = x

200

Convert the following to exponential form

log₆ 13 = n

6ⁿ=13

300

Evaluate 

log₂128

7

400

Given the logarithms below, which one does not equal the others?

log₃₄1                   ln 1

log₆₇1                   log 10

log 10 is 1 and the others have a value of 0

500

Given: log₄8 = a and log₄5 = b, which expression is equivalent to 40?

A)  4a + 4b          B) 4^ab                 C)  16^ab

D)  4^a+b                    E)  16ab          F)  16^a+b

D

Logarithmic Inverses & Graphs

100

What is the domain of exponential functions?

All real numbers

200

What is the range of logarithmic functions?

All real numbers

300

What is the inverse of y = 2^x

log₂x

400

What type of asymptotes do exponential functions have? (vertical or horizontal) 

horizontal asymptote

500

What is the domain of y = log_1/3x

x>0

Properties of Logarithms

100

Expand log₅ (17x²)

log₅17 + 2log₅x

200

Condense 

log₃ 67 - 2 log₃x + log₃y

log₃ (67y/x²) 

300

Expand 

log5²x⁴

2log5 + 4logx

400

Condense 

1/3log₄x + log₄y + 5log₄z

log₄ (x^1/3yz⁵)

500

Condense 

logx - 2logy + 3logz

log (xz^3/y^2)

Exponential and Logarithmic Equations

100

Solve

0.5^x=2^2x+7

x = -7/3

200

Solve

9^x-2=27^3x

x= -4/7

300

Solve 

log₆(5x - x²)=log₆(2x - 4)

x = 4

x = -1 is extraneous

400

Solve

log₂4 + log₂x = 6

x=16

500

Solve

5^x+3=10

x = -1.57