Exponentials and Logs

Exponential Fundamentals

100

Growth or decay?

1/2(3^x)

Growth

200

State the domain and range of the function:

f(x)=3(4)^x - 6

D: ARN

R: y>-6

300

State growth or decay:

y = 3(.85)^x

decay

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.

$37,178.31

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

(0, 7) and (5, 7168)

f(x) = 7(4^x)

500

Solve for x

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

x = 4

Pop Culture

100

The names of Gru's three adopted daughters in Despicable Me are what?

margo, edith and agnes

200

In what year was the first Apple iPhone released?

2007

300

How many NFL teams have bird mascots?

5

—Five (the Philadelphia Eagles, the Arizona Cardinals, the Atlanta Falcons, the Baltimore Ravens, and the Seattle Seahawks)

400

What is the most popular emoji on social media? Draw it.

Face with tears of joy

500

What is the name for a group of porcupines?

A prickle 

Geometric Sequences

100

What does the r stand for in a_n=a₁r^n-1

common ratio

200

Find the indicated term:

a₁=5

r=2

n=7

320

300

Find the a₁ term:

a₆=9216

r=4

n=6

a₁=9

400

Find the sum of the geometric series for which

a₁=15

r=2/3

n=5

1055/27 or 39.074...

500

What is the next term in the geometric sequence:

10, 5/2, 5/8, 5/32, ...

5/128