(1/4)^5 = 1/4 x 1/4 x 1/4 x 1/4 x 1/4  =  1/(4x4x4x4x4) = 1/1024

Another way:

Remaining = Original ( e^(-kt) )        where 'k' is  a decay constant

250 = 600 e^(-k * 20)        yields k = .0437734

1/2 of 600 is 300 so substitue to find 't1/2'

300 = 600 e^(-.0437734 *t) 

ln (300/600) = -.0437734 * t

t= 15.835 years                           (t1/2)

-1212(p+2) = -3 -p

-1212p - 2424 = -3 - p    add 1212 p to both sides

-2424 = -3 +1211p        Add 3 to both sides

-2421 = 1211p               divide both sides by 1211

-2421/1211 = p 

"Zeroes' are where the function equals zero.....if

x+ 6 = 0

x+8=0

or x+15 = 0    this function will equal zero

SOOOO if x= -6  or  -8  or -15    this function will equal zero and these are the 'zeroes' of this function.

You'll have to supply a value to 'k' to get a discrete ( 'defined' ) answer from a calculator....

I come up with 144.2 m      IF in your question, 31.5 m is actually 31.5 m/s

If , at its HIGHEST point , it is still moving 31.5 m/s that value must be the HORIZONTAL component of the initial velocity (as the vertical component is ZERO when at hightest point.

SO angle of shot is  53.7  cos(angle) = 31.5    Yields angle =  54.08 degrees

Then VERTICAL component is   53.7 sin(54.08) = 43.49 m/s

vf=vo + at       0 = 43.49 + (-9.81)t       yields t = 4.433 seconds

xf=xo + vo t + 1/2 a t^2                        yields xf = 144.2 m

I come up with 144.2 m      IF in your question, 31.5 m is actually 31.5 m/s

Happy Birthday !!!    I am going to celebrate  FOR you !....

LOL

x^(-6)  =  1/x^6        NOT  1/6x