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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

Where can you find the hypoglossal nerve?

Jaw/Throat

500

Name at least 2 professional Football, Baseball, Hockey, and Basketball teams from New England.

New England Patriots

Boston Red Sox

Boston Celtics

Boston Bruins

New England Revolution