Math 1150 Exponential and Logarithmic Jeopardy(kind of)!!!

Exponential Functions

100

What is an exponential function?

Any function of the form f(x) = a^x, where a > 0 and a not equal to 1. 

200

Graph f(x) = 3^x-4

Answer given by Shattuck

300

Graph g(x) = (1/2)^x+1 + 3 

Answer given by Shattuck

400

Find the ending amount of an investment of $10000 invested at 4% interest compounded monthly for 5 years.  

$12,209.97

500

Find the ending investment amount of $32,000 invested at 7% interest compounded continuously for 9 years.  

$60083.54

Logarithmic Functions

100

What is a logarithmic function?

Any function of the form f(x) = log_ax, where a>0 and a can't equal 1

200

Graph:   f(x) = log₂(x + 3) labeling all important concepts

Graph given by Shattuck

300

Simplify:    log₅(1/125)

-3

400

Condense into a single logarithm:

5 lnx - 4 lny + 2 lnz

ln(x⁵z²/y⁴)

500

Expand the following using properties A,B and C:

log[(2x+1)³/(5y-2)^1/2]

3log(2x+1) - (1/2)log(5y-2)

Exponential Equations

100

solve:

          3^{x + 4} =  81

x = 0

200

solve:

     4e^2x+1 = 12

x = [-1 + ln(3)]/2

300

Solve:

   e^2x - 3x - 4 = 0

x = ln(4)

400

Solve using natural logs:

4^x-2 =  3^{2x + 1}

x = ln48 / ln(4/9)

500

solve for t:

25000 = 5000(1 + .03/4)^4t

t = 54 years

Logarithmic Equations

100

Solve 

  log(3x + 3) = log(5x + 1) 

x = 1

200

 Solve 

   log₂(x - 3) = 5

x = 35

300

Solve:

  log₃(x) + log₃(x - 2) = 1

x = 3

400

Solve 

     log(4x - 2) -  log(2x + 1) = log(5)

No Solution

500

solve:

     (lnx)² = lnx

x = e, x = 1

Misc.

100

Exponential and Logarithmic Functions are _______

functions of each other as long as ____________. 

inverse

bases are the same

200

What is the transformation property?

log_ax = y    if and only if  a^y = x

300

UCM has had a zombie outbreak.  The outbreak started with 7 zombies, then after 8 days there were 120 zombies.  Assuming exponential growth, how many zombies are there after 20 days?

8517.38    parts of zombies makes sense!!

400

where can you follow the UCM esports team?

Twitter, Facebook, Instagram, Twitch and Discord

500

Simplify

(ln(e^{ln e}) + 10^log5  - 3log₅(5²)

0