CPhill

Thanks, PM........!!!!!

I'm assuming that your lunch break comes during the work hours

So....you really are paid for 4.5 hrs per day

So....the weekly amount is

4.5  *  5 *  15     =   $337.50

Equation of asymptote  :   y = -2

I believe the "parent" is     f(x) = (1/3)^x

This graph shifts the parent  down by  2 units

So.....the equation  of g(x)   is

g(x)   =  ( 1/3)^x  - 2

I assume this is

3x /   [ 2x^2 - 18 ]        if so, we can wrtite this as

(3x) ( 2x^2 - 18)^(-1)

First derivative

3 ( 2x^2 - 18)^(-1)  - 3x (2x^2 - 18)^(-2) (4x) =

3( 2x^2 - 18 )^(-1) - 12x^2 (2x^2 - 18)^(-2)   =

3 ( 2x^2 - 18)^(-2)    [ (2x^2 - 18 - 4x^2 ] =

3 (2x^2 - 18)^(-2) [ -2x^2 - 18 ] =

3 ( 2x^2 - 18)^(-2) [ -2 (x^2 + 9 ] =

-6 (x^2 + 9) (2x^2 - 18)^(-2)

Second derivative

- 6  [   2x (2x^2 - 18)^(-2)  - 2 (x^2 + 9) (2x^2 - 18)^(-3) (4x) ]   =

-6 [  2x (2x^2 - 18)^(-2)   - 8x (x^2 + 9) (2x^2 - 18)^(-3) ]  =

-6 [ 2x (2x^2 - 18)^(-3)  ] [   (2x^2 - 18) - 4( x^2 + 9) ]   =

-6 [ 2x (2x^2 - 18)^(-3) ]   [ 2x^2 - 18 - 4x^2 - 36 ]   =

-6 [ 2x (2x^2 - 18)^(-3) [ -2x^2 - 54 ]   =

6 [ 2x (2x^2 - 18)^(-3) (2)(x^2 + 27) ]  =

12 [ 2x (2x^2 - 18 )^(-3) (x^2 + 27)   =

24x (x^2 + 27) / [ (2^3 (x^2 - 9)^(-3) ] =

24x  (x^2 + 27) / [ 8 ( x^2 - 9)^(-3) ] \

3x (x^2 + 27) (x^2 - 9 )^(-3)

Yep...I joined in Mar 2014.....

As Melody said.....it used to be more "wacky".....before we got "grown-up".....

[ and more stodgy ]

LOL!!!!!

What do you think our probability of being correct is   ????

Here's my best attempt

Probability  that Badgers win at least 4 games   =

1 - Probability that they win < 4 games =

1 - [ C(7, 0) + C(7, 1) + C(7,2) + C(7, 3) ] * (1/2)^7  =   1/2

I agree with Melody

On the first 2008 flips.....each should have the same results

On the 2009th flip, Gimli has a (1/2) probability of getting a head

This seems too simple....usually, when that's so.....I've not considered some important aspect of the problem.....LOL!!!!

Thanks, Alan

Here's another method...."divide and average"

Since 1.5^2 = 2.25.....Let   us guess that the square root of 2   =  1.5    

[ This is arbitrary....we could pick another value, if we wished....the method will still work ]

Divide    2 /1.5    =  1.33

Average this with  1.5    =  [ 1.33 + 1.5] / 2   = 1.415

Divide   2 / 1.415   =  1.4134

Average this with 1.415  =  [ 1.415 + 1.4134 ] / 2   = 1.4142

Divide  2 / 1.4142   =  1.4142

We can stop here.....this = √2   to  4 decimal places....!!!!

We need an exponential growth model, here

The function that ost cosely mdels the data   is

f(x)   = 11.7588 ( 1.4094 )^x