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 house appreciates in value at a rate of 5% per year, compounded continuously. You bought it for $245,000.Write an eq to represent this situation where time, t, is in months.

y = 245,000e^(12(.05)/12)t

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

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

500

State the domain, range and eq of asymptote:

g(x) = 2log₄(x-5)+69

D: [5, in]

R: All reals

Asyp: x = 5

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

Solve for x:

ln(x+5)=3

x=15.09

500

Solve for x

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

x = 4

Pop Culture

100

Why was Greenland named as such?

Greenland is called Greenland because of a clever trick employed by Erik the Red, a Norse explorer, who was exiled from Iceland. He named the island "Grœnland" (Greenland) in Old Norse, hoping that the pleasant name would attract settlers to the land, despite it being mostly covered in ice and snow

200

In what year was the first Apple iPhone released?

2007

300

What is Mr. Aurelia's favorite sport and TV show?

Baseball and Dr. Who

pts also for hockey, the office, parks and rec, big bang

400

Name 3 Italian Brainrot characters

Ans will vary

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

Name every professional Football, Baseball, and Basketball and Hockey 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

NY Rangers

NI Islanders

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