ElectricPavlov

You should do the MULT FIRST then the SUBTR

6 - 56  = -50

4/ (3 (sqrt8)) === 4 / (3 sqrt(4x2)) =  4 / ((3x2)(sqrt2)) = 2/(3sqrt2) = 2 sqrt2 / (3 sqrt2 sqrt2) = 2 sqrt2 /6  = sqrt(2) / 3

Using a graphing calc I get   -1.196  as a zero

6.2 x 10^(-4)

Max is correct and gives the exact answer....which is the same answer I gave (rounded) as

.   sqrt(98) = sqrt(49 x 2) = 7  sqrt2 = 9.899 in

But your answer does not satisfy the given equation for decay...

the question CLEARLY states the amount of isotope is given by  85e^(-t/719)   where t is in years.

The ORIGINAL amount is given by t= 0      85

85e^((-1858.59)/719) = the amount at 1858.59 years = 6.4088   which is NOT 1/6 of 85 = 14.166

Just multiply both sides of the equation by 16 to find m !

1/6 (85) = 85 e^(-t/719)         this is of the form   A = Ao e^kt    where k= -.0013908

1/6 = e^(-t/719)

ln(1/6) = (-t/719)

-719 ln(1/6) = t     = 1288.28 years

Use pythagorean theorem   a^2 + b^2 = c^2      where c is the diagonal   and  a and b are the side lengths (both 7)

7^2 + 7^2 = c^2

49 + 49 = 98 = c^2    c = sqrt(98) = 9.899 in

K = -1/29    IS less than  0 

Ao = Ao e^(-t/29)

1/2Ao = e^(-t/29)

ln 1/2 = -t/29

ln 1/2  *  29  =  -t

t=20.10     is the half life

85   one half life  42.5    two half lives  21.25   three half lives  10.6.5      down to 8.5 is another partial half life

            20.1                 +     20.1                     +      20.1                          +     ~6      =  ~   66.3  years