Exponentials and Logs

Exponential Fundamentals

100

Growth or decay?

1/2(3^x)

Growth

200

In 2006, there were approximately 233 million cell phone subscribers in the United States. During the next 4 years, the number of cell phone subscribers increased by 6% each year.

Write an exponential growth model to represent the number y of subscribers t years after 2006

y = 233(1.06)^t

300

State the rate of increase or decrease.

y = 3(.85)^x

15% decrease

400

You start off with an account that has $32,000 and an annual interest rate of 5%. How much money will you have after 3 years if the account compounds daily? Round to the nearest cent.

$35,365.23

500

Your friend evaluates log₃729=6 and concludes that this could be written in exponential form as 6³=729. Is he correct? 

No. It would be written as 3⁶=729

Logarithmic Fundamentals

100

Rewrite as a logarithm 

5⁴ = 625

log₅(625) = 4

200

What is the base of log(x)

10

300

Evaluate

log⁡₂₅₆16= ?

1/2

400

Evaluate 

log_b(1) = ?

log_b(1) = 0

500

Evaluate 

log₄32= ?

5/2

Exp and Log Equations

100

Solve for x

5^2x = 5^x+1

x = 1

200

Solve for x

49^{6x + 1} = 343

x = 1/12

300

Solve for x

2(5)^3x+10-1=11

x = -3

400

Write an equation for the exponential graph that passes through the two points

(3, 448) and (5, 7168)

f(x) = 7(4^x)

500

Solve for x

log(3x) - log(x+8) = 0

x = 4

Pop Culture

100

What singer holds the record for most Grammy nominations? 

Beyonce (88 nominations)

200

What animal did Britney Spears famously carry on her shoulders during a performance?

A snake

300

What is the most watched video on YouTube?

Baby Shark Dance (11 billion views)

400

Which Kardashian created the denim brand Good American? 

Khloe Kardashian 

500

What show currently holds Netflix's all time viewership record?

Squid Games