Logs/Exponentials

Convert Forms

100

log(x)=10

10^10=x

200

e^x=5

ln(5)=x

300

2^5x=9

log₂(9)=5x

400

log_x(5)=13

x¹³=5

500

ln(2x-5)=4

e⁴=2x-5

Solving

100

Solve for x:

log₂(x)=5

x=32

200

Solve for x:

4^x - 4 = 12

x=2

300

Solve for x:

ln(x+5)=3

x=15.09

400

Solve using equivalent bases:

2^4x-1 = 16^2x

x=-0.25

500

Solve for x:

2^x=14^x

x=0

Features of Graphs

100

Write the domain of the function without graphing:

f(x)=5^x

x can be all real numbers

200

Determine the vertical asymptote of the function without graphing:

g(x) = log₄(x)+69

x=0

300

Determine the x and y intercepts of the function without graphing:

h(x)=4^x - 4

x intercept (1, 0)

y intercept (0, -3)

400

Which function has both an x and a y intercept? What are they?

g(x) = log₂(x) + 5

h(x) = 2^x - 4

f(x) = -x² - 8

h(x) has an x intercept at (2, 0) and a y intercept at (-3, 0)

500

Determine the end behavior of the function:

m(x) = log_1/2(x)

as x -> 0, m(x) -> infinity

as x -> infinity, m(x) -> negative infinity

Exponential Modeling

100

Your bank account gives you 2% interest every year. If you start this year with $200, how much will you have after 3 years?

$212.24

200

Your house appreciates in value at a rate of 5% per year, compounded continuously. You bought it for $245,000. What is it worth 8 years from now?

$365,497.05

300

You buy a car for $12,000. It depreciates at a rate of 3.2% compounded twice a year. What is it worth 4 years from now?

$10547.32

400

Your stock investment is currently worth $110, but it grows at a rate of 5.3% per year compounded every 3 months. How many years until the account is worth $800?

37.6839 years

500

Your motorcycle is currently worth $1,200 and it is depreciating at a rate of 4.4% per year compounded once every month. What was the motorcycle worth 7 years ago?

$1633.77

General Trivia

100

What year was the first Star Wars movie released?

1977

200

Name 3 countries that drive on the left side of the road

Examples:

UK, India, Japan, Australia, New Zealand

300

Which movie won the most oscars this year?

Everything, Everywhere, All at Once

400

What year was Mr. Lappin born in?

1999

500

Name every professional Football, Baseball, and Basketball team from the state of New York.

New York Giants

New York Jets

Buffalo Bills

New York Mets

New York Yankees

Brooklyn Nets

New York Knicks